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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-03</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001604477</issuerCik>
        <issuerName>SQZ Biotechnologies Co</issuerName>
        <issuerTradingSymbol>SQZ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340097</rptOwnerCik>
            <rptOwnerName>Invus Public Equities, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>750 LEXINGTON AVENUE 30TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001460839</rptOwnerCik>
            <rptOwnerName>Minne Pascal</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>8 CLOS DU BOCAGE, B-1332</rptOwnerStreet1>
            <rptOwnerStreet2>GENVAL, BELGIUM</rptOwnerStreet2>
            <rptOwnerCity></rptOwnerCity>
            <rptOwnerState>C9</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>BELGIUM</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001218180</rptOwnerCik>
            <rptOwnerName>Artal International S.C.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001522131</rptOwnerCik>
            <rptOwnerName>Artal International Management S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001053906</rptOwnerCik>
            <rptOwnerName>Artal Group S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001283968</rptOwnerCik>
            <rptOwnerName>Westend S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VALLEY PARK, 44,</rptOwnerStreet1>
            <rptOwnerStreet2>RUE DE LA VALLEE</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-2661</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001460840</rptOwnerCik>
            <rptOwnerName>Stichting Administratiekantoor Westend</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CLAUDE DEBUSSYLAAN, 46</rptOwnerStreet1>
            <rptOwnerStreet2>1082 MD AMSTERDAM</rptOwnerStreet2>
            <rptOwnerCity>THE NETHERLANDS</rptOwnerCity>
            <rptOwnerState>P7</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>NETHERLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001766952</rptOwnerCik>
            <rptOwnerName>Artal Treasury Ltd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.O. BOX 165</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 4, BOROUGH HOUSE, RUE DU PRE</rptOwnerStreet2>
            <rptOwnerCity>ST. PETER PORT</rptOwnerCity>
            <rptOwnerState></rptOwnerState>
            <rptOwnerZipCode>GY1 3JJ</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340096</rptOwnerCik>
            <rptOwnerName>Invus Public Equities Advisors, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>750 LEXINGTON AVENUE 30TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1141308</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1141308</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>465000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1606308</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Series C Convertible Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-11-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>843490</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>888194</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Series D Convertible Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-11-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>240375</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>253114</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On November 3, 2020, the Series C Convertible Preferred Stock and the Series D Convertible Preferred Stock each converted to Common Stock on a 1.0530 for 1 basis without payment of further consideration upon the closing of the Issuer's initial public offering.  The shares had no expiration date.</footnote>
        <footnote id="F2">The shares are held directly by Invus Public Equities, L.P. The general partner of Invus Public Equities, L.P. is Invus Public Equities Advisors, LLC. Artal Treasury Ltd is the managing member of Invus Public Equities Advisors, LLC. Artal Treasury Ltd is a wholly owned subsidiary of the Geneva branch of Artal International S.C.A. The managing partner of Artal International S.C.A. is Artal International Management S.A., which is a wholly owned subsidiary of Artal Group S.A. Westend S.A. is the parent company of Artal Group S.A., and the majority stockholder of Westend S.A. is Stichting Administratiekantoor Westend (&quot;Stichting&quot;).</footnote>
        <footnote id="F3">(Continued from Footnote 2) Mr. Pascal Minne is the sole member of the board of Stichting. Each of the Reporting Persons, other than Invus Public Equities L.P., disclaims beneficial ownership of the securities held by the other Reporting Persons, except to the extent of such Reporting Person's pecuniary interest therein, and, pursuant to Rule 16a-1(a)(4) under the Exchange Act, each of the Reporting Persons (other than to the extent it directly holds securities reported herein) states that the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all of the reported securities for purposes of Section 16 of the Exchange Act or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Invus Public Equities, L.P., By: Invus Public Equities Advisors, LLC, its General Partner, By: /s/ Raymond Debbane, President</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Invus Public Equities Advisors, LLC, By: /s/ Raymond Debbane, President</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal Treasury Ltd, By: /s/ Keith Le Poidevin, Director</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal International S.C.A., By: Artal International Management S.A., its Managing Partner, By: /s/ Anne Goffard, Managing Director</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal International Management S.A., By: /s/ Anne Goffard, Managing Director</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Artal Group S.A., By: /s/ Anne Goffard, Authorized Person</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Westend S.A., By: /s/ Pascal Minne, Director</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Stichting Administratiekantoor Westend, By: /s/ Pascal Minne, Sole Member of the Board</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Pascal Minne</signatureName>
        <signatureDate>2020-11-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
