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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-09-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001401708</issuerCik>
        <issuerName>NanoString Technologies Inc</issuerName>
        <issuerTradingSymbol>NSTG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001252522</rptOwnerCik>
            <rptOwnerName>GALAKATOS NICHOLAS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CLARUS VENTURES, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>101 MAIN STREET, SUITE 1210</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02142</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>2018-09-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>162408</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.448</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4121848</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-09-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>85823</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.99</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4036025</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrant (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>8.448</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-09-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>162408</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2011-11-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2018-11-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>162408.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Clarus Ventures II GP, L.P. (the &quot;GPLP&quot;), as the sole general partner of Clarus Lifesciences II, L.P. (&quot;Clarus&quot;), may be deemed to beneficially own certain of the shares held of record by Clarus. The GPLP disclaims beneficial ownership of all shares held of record by Clarus in which the GPLP does not have an actual pecuniary interest. Clarus Ventures II, LLC (the &quot;GPLLC&quot;), as the sole general partner of the GPLP, may be deemed to beneficially own certain of the shares held of record by Clarus. The GPLLC disclaims beneficial ownership of all shares held of record by Clarus in which it does not have an actual pecuniary interest.  Each of Nicholas Galakatos, a member of the board of directors, and Messrs. Henner, Liptak, Simon and Wheeler, as individual Managing Directors of the GPLLC, may be deemed to beneficially own certain of the shares held of record by Clarus.</footnote>
        <footnote id="F2">Each of Messrs. Galakatos, Henner, Liptak, Simon and Wheeler disclaims beneficial ownership of all shares held of record by Clarus in which he does not have an actual pecuniary interest.</footnote>
        <footnote id="F3">On September 17, 2018 Clarus Lifesciences II, L.P. (&quot;Clarus&quot;) exercised warrants to purchase 162,408 shares of the Company's common stock for $8.448 per share. Clarus paid the exercise price on a cashless basis, resulting in the Company's withholding of 85,823 of the warrant shares to pay the exercise price and issuing to Clarus the remaining 76,585 shares.</footnote>
        <footnote id="F4">Pursuant to the terms of a Lock-up Agreement executed by the Reporting Person, a member of the board of directors, in favor of the underwriters of the Company's public offering in July 2018 (the &quot;Lock-up&quot;), the Company withheld the number of shares set forth above pursuant to a net settlement permitted under the terms of the Lock-up. No shares were sold by the Reporting Person or Clarus in connection with the exercise and the common shares issued as a result of the exercise are subject to the terms of the Lock-up.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shannon Atchison, Attorney-in-fact</signatureName>
        <signatureDate>2018-09-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
