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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001620533</issuerCik>
        <issuerName>Shake Shack Inc.</issuerName>
        <issuerTradingSymbol>SHAK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001452724</rptOwnerCik>
            <rptOwnerName>Lyons Jenna</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SHAKE SHACK INC.,</rptOwnerStreet1>
            <rptOwnerStreet2>225 VARICK STREET, SUITE 301</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10014</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>CLASS A COMMON STOCK</value>
            </securityTitle>
            <transactionDate>
                <value>2020-06-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1476</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>57.17</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3592</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of Class A Common Stock (&quot;Class A Stock&quot;) of Shake Shack Inc. (the &quot;Issuer&quot;) underlying restricted stock units acquired by the Reporting Person. On June 10, 2020, pursuant to the Issuer's 2015 Incentive Award Plan, as amended, the Issuer's Non-Employee Director Compensation Policy, and the recent approval of the Board of Directors of the Issuer dated June 10, 2020 as reflected in the Current Report on Form 8-K filed with the Securities and Exchange Commission on June 12, 2020,  the Reporting Person was awarded restricted stock units that represent the right to receive Class A Stock of the Issuer. The restricted stock units representing the right to receive Class A Stock of the Issuer vest on June 10, 2021, subject to the Reporting Person's continued service with the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ronald Palmese, Jr., Esq., Attorney-in-Fact for Jenna Lyons</signatureName>
        <signatureDate>2020-06-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
