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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-04-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001890988</rptOwnerCik>
            <rptOwnerName>Sanberg Joseph N.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>528 PALISADES DRIVE, #545</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PACIFIC PALISADES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90272</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001890968</rptOwnerCik>
            <rptOwnerName>RJB Partners LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O JOSEPH N. SANBERG</rptOwnerStreet1>
            <rptOwnerStreet2>528 PALISADES DRIVE, #545</rptOwnerStreet2>
            <rptOwnerCity>PACIFIC PALISADES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90272</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>2022-04-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1666667</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.00</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8386593</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By RJB Partners LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-04-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1666666</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.00</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1666666</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Long Live Bruce, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>214293</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1250</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Aspiration Growth Opportunities II GP, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrant (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-04-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2022-02-14</value>
            </exerciseDate>
            <expirationDate>
                <value>2029-02-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>250000</value>
                    <footnoteId id="F6"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By RJB Partners LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Warrant (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2022-02-14</value>
            </exerciseDate>
            <expirationDate>
                <value>2029-02-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>35714</value>
                    <footnoteId id="F6"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By RJB Partners LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In connection with the closing of the acquisitions of securities contemplated by that certain purchase agreement, dated as of April 29, 2022 (the &quot;Purchase Agreement&quot;), RJB Partners LLC (&quot;RJB Partners&quot;), of which Mr. Joseph N. Sanberg is managing member, agreed to purchase from the Issuer, for an aggregate purchase price of $40 million, 3,333,333 shares of Class A common stock, 1,666,666 of which shares (the &quot;Initial Shares&quot;) were acquired on April 29, 2022 in connection with the closing of the initial acquisition of securities contemplated by the Purchase Agreement and the remaining 1,666,667 of such shares will be acquired by RJB Partners on May 30, 2022 (or such other date as mutually agreed by RJB Partners and the Issuer), subject to customary closing conditions.</footnote>
        <footnote id="F2">(Continued from footnote 1) On April 29, 2022, RJB Partners assigned to Long Live Bruce, LLC, an entity owned indirectly by Mr. Joseph N. Sanberg (&quot;Long Live Bruce&quot;), as the managing member of Long Live Bruce, its right to acquire the Initial Shares and Long Live Bruce assumed RJB Partners' obligations in respect of the Initial Shares, including the payment of the purchase price thereof.</footnote>
        <footnote id="F3">These securities are owned directly by RJB Partners, a 10% owner of the Issuer, and owned indirectly by Mr. Joseph N. Sanberg, as the managing member of RJB Partners.  Mr. Joseph N. Sanberg disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all the reported securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F4">These securities are owned directly by Long Live Bruce, and owned indirectly by Mr. Joseph N. Sanberg, as the managing member of Long Live Bruce.  Mr. Joseph N. Sanberg disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all the reported securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F5">These securities are owned directly by Aspiration Growth Opportunities II GP, LLC (&quot;AGO II&quot;), and owned indirectly by Mr. Joseph N. Sanberg, as the managing member of AGO II.  Mr. Joseph N. Sanberg disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of all the reported securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F6">In connection with obtaining financing to consummate the transactions contemplated by the Purchase Agreement, RJB Partners agreed to transfer warrants exercisable for an aggregate 250,000 shares of Class A common stock of the Issuer at an exercise price of $15 per share (the &quot;$15 Warrants&quot;) to certain affiliates of Metropolitan Partners Group. As a result of the transfer of the $15 Warrants described in the foregoing sentence, RJB Partners owns $15 Warrants exercisable for an aggregate of 35,714 shares of Class A common stock, which number is subject to adjustment in certain circumstances in accordance with the terms of the $15 Warrants.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Joseph N. Sanberg</signatureName>
        <signatureDate>2022-05-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>RJB Partners LLC, /s/ Joseph N. Sanberg, Name:	Joseph N. Sanberg, Title: Managing Member</signatureName>
        <signatureDate>2022-05-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
