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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-07-21</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001845290</issuerCik>
        <issuerName>Macquarie Infrastructure Holdings, LLC</issuerName>
        <issuerTradingSymbol>MIC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001418333</rptOwnerCik>
            <rptOwnerName>MACQUARIE GROUP LTD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LEVEL 6, 50 MARTIN PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>SYDNEY, NEW SOUTH WALES 2000</rptOwnerStreet2>
            <rptOwnerCity>AUSTRALIA</rptOwnerCity>
            <rptOwnerState>C3</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>AUSTRALIA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001311388</rptOwnerCik>
            <rptOwnerName>Macquarie Infrastructure Management (USA) INC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>125 W. 55TH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Unit</value>
            </securityTitle>
            <transactionDate>
                <value>2022-07-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>15235184</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.11</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="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects securities disposed of pursuant to the terms of the Agreement and Plan of Merger, dated as of June 14, 2021 (the &quot;Merger Agreement&quot;), by and among the Issuer, AMF Hawaii Holdings, LLC, AMF Hawaii Merger Sub, LLC, and other parties thereto, which closed on July 21, 2022. Pursuant to the terms of the Merger Agreement, each Issuer common unit (other than certain excluded common units) was canceled and converted into the right to receive $4.11 in cash without interest.</footnote>
        <footnote id="F2">Includes 15233084 shares that were held by Macquarie Infrastructure Management (USA) Inc., a subsidiary of Macquarie Group Limited, and 2100 shares that were held in various investment funds for which Macquarie Investment Management Global Limited, a subsidiary of Macquarie Group Limited, acts as investment advisor. The reporting persons disclaim any beneficial ownership of all such securities except to the extent of their pecuniary interest in such shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>MGL, MIMUSA, - /s/ Charles Glorioso, Authorized Signatory, /s/Gus Wong, Authorized Signatory</signatureName>
        <signatureDate>2022-07-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
