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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-02-26</periodOfReport>

    <notSubjectToSection16>0</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 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>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>2019-02-26</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>15000000</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15000000</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>2019-02-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>15000000</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.15</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-02-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>15000000</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>15000000</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21287771</value>
                    <footnoteId id="F5"/>
                </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 26, 2019, Bessemer Venture Partners VIII L.P. (&quot;BVP VIII&quot;) sold 6,809,971 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 8,190,029 shares of Class A Common Stock, each at a single execution price of $1.15 per share of Class A Common Stock.</footnote>
        <footnote id="F3">Represents 6,809,971 shares converted from Class B Common Stock to Class A Common Stock by BVP VIII and 8,190,029 shares converted from Class B Common Stock to Class A Common Stock by BVP VIII Inst. After the foregoing conversion, BVP VIII and BVP VIII Inst own 6,809,971 shares and 8,190,029 shares, respectively, of Class A Common Stock.</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>
        <footnote id="F5">After the foregoing conversion, BVP VIII and BVP VIII Inst own 9,664,606 shares and 11,623,165 shares, respectively, of Class B Common Stock.</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>2019-02-28</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>2019-02-28</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>2019-02-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Scott Ring, General Counsel, Deer VIII &amp; Co. Ltd</signatureName>
        <signatureDate>2019-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
