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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-01-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001677576</issuerCik>
        <issuerName>INNOVATIVE INDUSTRIAL PROPERTIES INC</issuerName>
        <issuerTradingSymbol>IIPR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001298786</rptOwnerCik>
            <rptOwnerName>Gold Alan D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O INNOVATIVE INDUSTRIAL PROPERTIES</rptOwnerStreet1>
            <rptOwnerStreet2>11440 WEST BERNARDO COURT, SUITE 220</rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92127</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Chairman</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-01-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12412</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>45.39</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>301455</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33750</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Children's Trust No. 1</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33750</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Children's Trust No. 2</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">An irrevocable trust of which a family member of the reporting person is a trustee and of which one of the reporting person's adult children is the sole beneficiary.</footnote>
        <footnote id="F2">Represents payment of tax liability by the forfeiture of shares of common stock to the company incident to the vesting of the reporting person's restricted stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brian J. Wolfe, Attorney-in-Fact</signatureName>
        <signatureDate>2019-01-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
