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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-12-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001104506</issuerCik>
        <issuerName>INSMED INC</issuerName>
        <issuerTradingSymbol>INSM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001506413</rptOwnerCik>
            <rptOwnerName>Whitten Timothy</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O INSMED INCORPORATED</rptOwnerStreet1>
            <rptOwnerStreet2>9 DEER PARK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>MONMOUTH JUNCTION</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>08852</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option - Right to Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.03</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2011-12-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>103100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.03</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2012-12-21</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-12-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>103100</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>332500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This Option shall be exercisable with respect to twenty-five percent (25%) of the shares of Common Stock subject to this Option on the first anniversary of the Date of Grant and with respect to an additional twelve and a half percent (12.5%) of the shares of Common Stock subject to this Option on the sixth month anniversary of the First Anniversary Date and each sixth month anniversary date thereafter through the fourth anniversary of the Date of Grant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Timothy Whitten</signatureName>
        <signatureDate>2011-12-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
