<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-08-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000310764</issuerCik>
        <issuerName>STRYKER CORP</issuerName>
        <issuerTradingSymbol>SYK</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
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            <rptOwnerName>STRYKER RONDA E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>1941 STRYKER WAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PORTAGE</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>49002</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
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    </reportingOwner>

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                    <value>By Revocable Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12177521</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By L. Lee Stryker Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>762</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>37600</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By 1988 William D. Johnston Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $331.15 to $332.11, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F2">Includes 560 shares previously held directly which were transferred to the Revocable Trust on August 18, 2026.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $332.17 to $333.085, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F4">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $333.16 to $334.14, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F5">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $334.21 to $335.145, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F6">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $335.15 to $336.145, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F7">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $336.15 to $337.145, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F8">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $337.15 to $338.13, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F9">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $338.15 to $339.10, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F10">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $331.74 to $332.00, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F11">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $332.81 to $333.775, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F12">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $333.81 to $334.20, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F13">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $335.05 to $335.06, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F14">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $336.20 to $337.14, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F15">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $337.31 to $338.255, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F16">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $338.30 to $339.295, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F17">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $339.30 to $340.295, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F18">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $340.30 to $341.27, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F19">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $341.30 to $342.295, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F20">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $342.32 to $343.29, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F21">The price reported in Column 4 is a weighted average sale price. The shares of Common Stock were sold in multiple transactions at prices ranging from $343.31 to $343.90, inclusive. The Reporting Person undertakes to provide upon request by the staff of the Securities &amp; Exchange Commission, the Issuer or any security holder of the Issuer, full information regarding the number of shares of Common Stock sold at each separate price within the range set forth herein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Austin Y. Ke, attorney-in-fact for Ronda E. Stryker</signatureName>
        <signatureDate>2026-08-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
