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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2020-10-29</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001021944</rptOwnerCik>
            <rptOwnerName>Temasek Holdings (Private) Ltd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>60B ORCHARD ROAD, #06-18 TOWER 2</rptOwnerStreet1>
            <rptOwnerStreet2>THEATRIUM@ORCHARD</rptOwnerStreet2>
            <rptOwnerCity>SINGAPORE</rptOwnerCity>
            <rptOwnerState>U0</rptOwnerState>
            <rptOwnerZipCode>233891</rptOwnerZipCode>
            <rptOwnerStateDescription>SINGAPORE</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series D Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1888924</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See note</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Series D Preferred Stock is convertible into Common Stock on a 1:1 basis at any time upon the holder's election and has no expiration date. All shares of Series D Preferred Stock shall be automatically converted into shares of Common Stock upon the closing of the Issuer's initial public offering.</footnote>
        <footnote id="F2">The shares are held of record by Elbrus Investments Pte. Ltd. (&quot;Elbrus&quot;). Elbrus is a direct wholly owned subsidiary of Temasek Life Sciences Private Limited, which in turn is a direct wholly owned subsidiary of Fullerton Management Pte Ltd, which in turn is a direct wholly owned subsidiary of Temasek Holdings (Private) Limited (&quot;Temasek&quot;). Therefore, Temasek may be deemed to beneficially own the shares held of record by Elbrus.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>TEMASEK HOLDINGS (PRIVATE) LIMITED, By: /s/ Gregory Tan, in his capacity as Authorized Signatory</signatureName>
        <signatureDate>2020-10-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
