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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-06-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000875355</issuerCik>
        <issuerName>INSIGNIA SYSTEMS INC/MN</issuerName>
        <issuerTradingSymbol>ISIG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001617807</rptOwnerCik>
            <rptOwnerName>Groveland Capital LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3033 EXCELSIOR BOULEVARD, SUITE 560</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MINNEAPOLIS</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55416</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5319</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5319</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>422000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.16</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-12-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2014-12-08</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-12-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reported securities are owned directly by Nicholas J. Swenson, who is a Director of the issuer.</footnote>
        <footnote id="F2">Each of the Reporting Persons may be deemed to be a member of a Section 13(d) group disclosed in a Schedule 13D filed on behalf of the Reporting Persons and Air T, Inc., the other member of such group, on August 18, 2014.  The members of this Section 13(d) group collectively own more than 10% of the Issuer's outstanding shares of Common Stock.  Each of the Reporting Persons disclaims beneficial ownership of the shares of Common Stock held by the other members of this Section 13(d) group except to the extent of his or its pecuniary interest therein.  The securities reported herein do not include any securities held by Air T, Inc., as such shares have been reported in a separate filing.</footnote>
        <footnote id="F3">This Form 4 is filed by Groveland Capital LLC (&quot;Groveland Capital&quot;), Groveland Hedged Credit Fund LLC (&quot;Groveland Fund&quot;) and Nicholas J. Swenson (collectively, the &quot;Groveland Group&quot;).  Groveland Capital serves as the investment adviser and general partner to the Groveland Fund and may direct the vote and disposition of the shares of Common Stock held by the Groveland Fund.  Mr. Swenson is the Managing Member of Groveland Capital and may direct Groveland Capital to direct the vote and disposition of the shares of Common Stock held by the Groveland Fund.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Groveland Hedged Credit Fund LLC, By:  /s/ Nicholas J. Swenson, Managing Member</signatureName>
        <signatureDate>2015-06-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Groveland Capital LLC, By:  /s/ Nicholas J. Swenson, Managing Member</signatureName>
        <signatureDate>2015-06-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Nicholas J. Swenson</signatureName>
        <signatureDate>2015-06-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
