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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-08-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000275053</issuerCik>
        <issuerName>NATURES SUNSHINE PRODUCTS INC</issuerName>
        <issuerTradingSymbol>NATR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001357553</rptOwnerCik>
            <rptOwnerName>Bunker Stephen M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>75 EAST 1700 SOUTH</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PROVO</rptOwnerCity>
            <rptOwnerState>UT</rptOwnerState>
            <rptOwnerZipCode>84606</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, CFO, Treasurer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>14.52</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-08-01</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>26250</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-02-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>26250</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option grant was approved by the board of directors of Nature's Sunshine Products, Inc. (the &quot;Company&quot;) on March 1, 2012, subject to shareholder approval of the stock option plan under which the option was granted.  The Company's shareholders approved the plan on August 1, 2012.  The option grant includes an additional 8,750 shares which will vest, if at all, upon achievement of certain performance conditions.</footnote>
        <footnote id="F2">Vests as follows:  25% on March 1, 2013; 25% on March 1, 2014; 25% on March 1, 2015; and 25% on March 1, 2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jamon A. Jarvis as Attorney-in-Fact for Stephen M. Bunker</signatureName>
        <signatureDate>2012-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
