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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001175522</rptOwnerCik>
            <rptOwnerName>SOKOLOFF JONATHAN D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11111 SANTA MONICA BOULEVARD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2000</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90025</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-06-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>379</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1411</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>832303</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>34.62</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-05-19</value>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2026-05-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2003</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10254</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>21.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2016-01-29</value>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-01-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>8251</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10254</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F7"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>595110</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F10"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of Class A common stock, par value $0.001 per share (&quot;A-Common&quot;) of the Issuer underlying restricted stock units awarded to the reporting person pursuant to the Issuer's 2015 Incentive Award Plan, as amended, and the Issuer's Non-Employee Director Compensation Policy on June 11, 2019.  The restricted stock units represent the right to receive shares of A-Common and vest on June 11, 2020, subject to the reporting person's continued service with the Issuer.</footnote>
        <footnote id="F2">Of the 1,411 shares of A-Common reported, 1,032 are vested and 379 will vest on June 11, 2020.</footnote>
        <footnote id="F3">Represents shares owned by Green Equity Investors VI, L.P. (&quot;GEI VI&quot;), Green Equity Investors Side VI, L.P. (&quot;GEI Side VI&quot;), and LGP Malted Coinvst LLC (&quot;Malted&quot;). Of the shares of A-Common reported, 300,615 are owned by GEI VI, 509,744 are owned by GEI Side VI, and 21,944 are owned by Malted.</footnote>
        <footnote id="F4">Mr. Sokoloff directly (whether through ownership or position), or indirectly through one or more intermediaries, may be deemed for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, to be the indirect beneficial owner of the shares owned by GEI VI, GEI Side VI, and Malted. Mr. Sokoloff disclaims beneficial ownership of the shares owned by each of GEI VI, GEI Side VI, and Malted, except to the extent of his pecuniary interest in GEI VI and GEI Side VI, and this report shall not otherwise be deemed an admission that he is the beneficial owner of such securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F5">These options are fully vested.</footnote>
        <footnote id="F6">The options reported on this row were granted in respect of Mr. Sokoloff's service on the Issuer's board of directors and are held by Mr. Sokoloff for the benefit of Leonard Green &amp; Partners, L.P.  Of the 10,254 options reported, 8,251 vested on January 29, 2016 and 2,003 vested on May 19,
2017.</footnote>
        <footnote id="F7">Pursuant to the terms of the Amended and Restated Certificate of Incorporation of the Issuer, shares of B-Common can be paired with LLC Interests on a one-to-one basis and tendered to the Issuer in exchange for shares of A-Common (or cash, at the Issuer's election).</footnote>
        <footnote id="F8">Not applicable.</footnote>
        <footnote id="F9">Represents shares of B-Common owned by GEI VI and Malted. Of the shares of B-Common reported on this row, 554,633 are owned by GEI VI and 40,477 are owned by Malted.</footnote>
        <footnote id="F10">Mr. Sokoloff directly (whether through ownership or position), or indirectly through one or more intermediaries, may be deemed for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, to be the indirect beneficial owner of the Equity Interests. Mr. Sokoloff disclaims beneficial ownership of the Equity Interests held by each of GEI VI, GEI Side VI, and Malted except to the extent of his pecuniary interest in GEI VI and GEI Side VI, and this report shall not otherwise be deemed an admission that he is the beneficial owner of such securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Andrew C. Goldberg, attorney-in-fact</signatureName>
        <signatureDate>2019-06-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
