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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-08-03</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>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12641</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.46</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2382344</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>37359</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.28</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2344985</value>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>43335</value>
                    <footnoteId id="F8"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.03</value>
                    <footnoteId id="F9"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2301650</value>
                    <footnoteId id="F10"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6666</value>
                    <footnoteId id="F11"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.86</value>
                    <footnoteId id="F12"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2294984</value>
                    <footnoteId id="F13"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </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="F14"/>
            </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="F15"/>
                </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="F16"/>
            </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="F15"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F17"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F17"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F18"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F17"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3299900</value>
                    <footnoteId id="F19"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F20"/>
                </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;) sold 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 Coinvest LLC (&quot;Malted&quot;). Of the shares of A-Common sold, 7,574 were sold by GEI VI, 4,514 were sold by GEI Side VI, and 553 were sold by Malted. GEI VI's, GEI Side VI's, and Malted's A-Common, together with GEI VI's and Malted's B-Common and LLC Interests, are collectively referred to herein as the &quot;Equity Interests.&quot;</footnote>
        <footnote id="F2">This transaction was executed in multiple trades at prices ranging from $37.87 to $38.86. The price reported above reflects the weighted average sale price. Mr. Sokoloff hereby undertakes to provide upon request to the SEC staff, the Issuer, or a security holder of the Issuer, full information regarding the number of Shares and prices at which the trades were effected.</footnote>
        <footnote id="F3">Represents shares owned by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common reported, 334,497 are owned by GEI VI, 2,029,148 are owned by GEI Side VI, and 18,699 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">Represents shares of A-Common sold by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common sold, 22,384 were sold by GEI VI, 13,341 were sold by GEI Side VI, and 1,634 were sold by Malted.</footnote>
        <footnote id="F6">This transaction was executed in multiple trades at prices ranging from $38.89 to $39.65. The price reported above reflects the weighted average sale price. Mr. Sokoloff hereby undertakes to provide upon request to the SEC staff, the Issuer, or a security holder of the Issuer, full information regarding the number of Shares and prices at which the trades were effected.</footnote>
        <footnote id="F7">Represents shares owned by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common reported, 312,113 are owned by GEI VI, 2,015,807 are owned by GEI Side VI, and 17,065 are owned by Malted.</footnote>
        <footnote id="F8">Represents shares of A-Common sold by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common sold, 25,965 were sold by GEI VI, 15,475 were sold by GEI Side VI, and 1,895 were sold by Malted.</footnote>
        <footnote id="F9">This transaction was executed in multiple trades at prices ranging from $38.55 to $39.54. The price reported above reflects the weighted average sale price. Mr. Sokoloff hereby undertakes to provide upon request to the SEC staff, the Issuer, or a security holder of the Issuer, full information regarding the number of Shares and prices at which the trades were effected.</footnote>
        <footnote id="F10">Represents shares owned by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common reported, 286,148 are owned by GEI VI, 2,000,332 are owned by GEI Side VI, and 15,170 are owned by Malted.</footnote>
        <footnote id="F11">Represents shares of A-Common sold by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common sold, 3,995 were sold by GEI VI, 2,380 were sold by GEI Side VI, and 291 were sold by Malted.</footnote>
        <footnote id="F12">This transaction was executed in multiple trades at prices ranging from $39.69 to $39.98. The price reported above reflects the weighted average sale price. Mr. Sokoloff hereby undertakes to provide upon request to the SEC staff, the Issuer, or a security holder of the Issuer, full information regarding the number of Shares and prices at which the trades were effected.</footnote>
        <footnote id="F13">Represents shares owned by GEI VI, GEI Side VI, and Malted. Of the shares of A-Common reported, 282,153 are owned by GEI VI, 1,997,952 are owned by GEI Side VI, and 14,879 are owned by Malted.</footnote>
        <footnote id="F14">These options will vest on May 19, 2017.</footnote>
        <footnote id="F15">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 will vest on May 19,
2017.</footnote>
        <footnote id="F16">These options vested on January 29, 2016.</footnote>
        <footnote id="F17">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="F18">Not applicable.</footnote>
        <footnote id="F19">Represents shares of B-Common owned by GEI VI and Malted. Of the shares of B-Common reported on this row, 3,070,099 are owned by GEI VI and 229,801 are owned by Malted.</footnote>
        <footnote id="F20">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/ Lance J.T. Schumacher, attorney-in-fact</signatureName>
        <signatureDate>2016-08-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
