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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001649094</issuerCik>
        <issuerName>Vaxcyte, Inc.</issuerName>
        <issuerTradingSymbol>PCVX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001886794</rptOwnerCik>
            <rptOwnerName>Dhaliwal Harpreet S.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VAXCYTE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>825 INDUSTRIAL ROAD, STE. 300</rptOwnerStreet2>
            <rptOwnerCity>SAN CARLOS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94070</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Technical Ops Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9743</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.689</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23928</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported is a weighted-average price. The shares were sold at prices ranging from $46.42 to $47.155. The reporting person will provide upon request to the SEC, the issuer or security holder of the
issuer, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F2">Includes one (1) share acquired on November 17, 2025 under the Issuer's Employee Stock Purchase Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Harpreet S. Dhaliwal, by /s/ Peter N. Efremenko, Attorney-In-Fact</signatureName>
        <signatureDate>2026-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
