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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-05-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001520697</issuerCik>
        <issuerName>Acadia Healthcare Company, Inc.</issuerName>
        <issuerTradingSymbol>ACHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001421620</rptOwnerCik>
            <rptOwnerName>WAUD REEVE B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WAUD CAPITAL PARTNERS, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-05-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2303</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30618</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>506844</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares will vest over a 3-year period in equal annual installments beginning May 19, 2023.</footnote>
        <footnote id="F2">The shares are owned of record as follows: (i) 157,491 shares by the Halcyon Exempt Family Trust (the &quot;Halcyon Trust&quot;), (ii) 37,493 shares by Waud Capital Partners, L.L.C. (&quot;WCP LLC&quot;), (iii) 155,930 shares by the 2012 RBW Jr Family Trust, and (iv) 155,930 shares by the Cecily R.M. Waud 2012 Family Trust (the &quot;2012 CRMW Family Trust&quot;).</footnote>
        <footnote id="F3">Mr. Waud may be deemed to beneficially own the shares of common stock described in Footnote (2) above by virtue of (A) his being the investment advisor of the Halcyon Trust of which Mr. Waud's children are beneficiaries, (B) his being the sole manager of WCP LLC, and (C) his being the investment advisor of the 2012 RBW Jr Family Trust and the 2012 CRMW Family Trust of which Mr. Waud's grandchildren are beneficiaries.</footnote>
        <footnote id="F4">Mr. Waud expressly disclaims beneficial ownership of the reported shares except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Reeve B. Waud</signatureName>
        <signatureDate>2022-05-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
