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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-10-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000842517</issuerCik>
        <issuerName>IBT BANCORP INC /MI/</issuerName>
        <issuerTradingSymbol>IBTB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001354537</rptOwnerCik>
            <rptOwnerName>Caul Sandra L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PO BOX 100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MT. PLEASANT</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48858</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2006-10-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>204.762</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>204.762</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>633.334</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">(1) Each share of phantom stock represents the right to receive one share of IBT Bancorp stock.</footnote>
        <footnote id="F2">(2) Shares of phantom stock are payable in cash following termination of the reporting person's employment wsith IBT Bancorp.  The reporting person may transfer his phantom stock account into an alternative investment account at any time.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Sandra L. Caul</signatureName>
        <signatureDate>2006-10-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
