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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-02-20</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001701114</issuerCik>
        <issuerName>Blue Apron Holdings, Inc.</issuerName>
        <issuerTradingSymbol>APRN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001508900</rptOwnerCik>
            <rptOwnerName>Bessemer Venture Partners VIII L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BESSEMER VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>1865 PALMER AVE., SUITE 104</rptOwnerStreet2>
            <rptOwnerCity>LARCHMONT</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10538</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001508902</rptOwnerCik>
            <rptOwnerName>Bessemer Venture Partners VIII Institutional L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BESSEMER VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>1865 PALMER AVENUE, SUITE 104</rptOwnerStreet2>
            <rptOwnerCity>LARCHMONT</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10538</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001559306</rptOwnerCik>
            <rptOwnerName>Deer VIII &amp; Co. L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BESSEMER VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>1865 PALMER AVENUE, SUITE 104</rptOwnerStreet2>
            <rptOwnerCity>LARCHMONT</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10538</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001559311</rptOwnerCik>
            <rptOwnerName>Deer VIII &amp; Co. Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BESSEMER VENTURE PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>1865 PALMER AVENUE, SUITE 104</rptOwnerStreet2>
            <rptOwnerCity>LARCHMONT</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10538</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1419184</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1419184</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1419184</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-02-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1419184</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1419184</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of Class B Common Stock is convertible into one share of Class A Common Stock at the option of the holder without payment or consideration and has no expiration date.</footnote>
        <footnote id="F2">On February 20,2020, Bessemer Venture Partners VIII L.P. (&quot;BVP VIII&quot;) sold 644,307 shares of Class A Common Stock and Bessemer Venture Partners VIII Institutional L.P. (&quot;BVP VIII Inst&quot; and together with BVP VIII, the &quot;BVP VIII Funds&quot;) sold 774,877 shares of Class A Common Stock, each at a single execution price of $3.25 per share of Class A Common Stock.</footnote>
        <footnote id="F3">Represents 644,307 shares converted from Class B Common Stock to Class A Common Stock by BVP VIII and 774,877 shares converted from Class B Common Stock to Class A Common Stock by BVP VIII Inst.</footnote>
        <footnote id="F4">Deer VIII &amp; Co. Ltd. (&quot;Deer VIII Ltd&quot;) is the general partner of Deer VIII &amp; Co. L.P. (&quot;Deer VII LP&quot; and, together with the BVP VIII Funds and Deer VIII Ltd, the &quot;BVP Entities&quot;), which is the general partner of the BVP VIII Funds. Deer VIII Ltd and Deer VIII LP disclaim beneficial ownership of the securities held by the BVP VIII Funds, and this report shall not be deemed an admission that Deer VIII Ltd and Deer VIII LP are the beneficial owners of such securities, except to the extent of their pecuniary interest therein, if any, by virtue of their direct and indirect general partner interests in the BVP VIII Funds.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Scott Ring, General Counsel, Deer VIII &amp; Co. Ltd., the General Partner of Deer VIII &amp; Co. L.P., the General Partner of Bessemer Venture Partners VIII L.P.</signatureName>
        <signatureDate>2020-02-24</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Scott Ring, General Counsel, Deer VIII &amp; Co. Ltd., the General Partner of Deer VIII &amp; Co. L.P., the General Partner of Bessemer Venture Partners VIII Institutional L.P.</signatureName>
        <signatureDate>2020-02-24</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Scott Ring, General Counsel, Deer VIII &amp; Co. Ltd., the General Partner of Deer VIII &amp; Co. L.P.</signatureName>
        <signatureDate>2020-02-24</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Scott Ring, General Counsel, Deer VIII &amp; Co. Ltd.</signatureName>
        <signatureDate>2020-02-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
