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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-31</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001618561</issuerCik>
        <issuerName>Nexvet Biopharma plc</issuerName>
        <issuerTradingSymbol>NVET</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001453077</rptOwnerCik>
            <rptOwnerName>Hirsch Daniel J.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FARALLON CAPITAL MANAGEMENT, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>ONE MARITIME PLAZA, SUITE 2100</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94111</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of Group Owning 10%</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.001 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Daniel J. Hirsch (&quot;Hirsch&quot;) previously filed Form 3s and Form 4s with respect to securities of the Issuer owned directly by Akubra Investors, LLC (&quot;Akubra&quot;), Bushranger Funding, LLC (&quot;Bushranger&quot;),  Ute Holdings, LLC (&quot;Ute&quot; and, together with Akubra and Bushranger, the &quot;Farallon SPVs&quot;).</footnote>
        <footnote id="F2">The members of Akubra are FCIP XR 2014, L.L.C. (&quot;FCIP XR&quot;) and Noonday Special Situation Partners, L.P. (&quot;NSSP&quot;) (each, a &quot;Farallon Akubra Fund&quot;). As the general partner of NSSP, NGP, L.L.C. (the &quot;NSSP General Partner&quot;) may be deemed to be a beneficial owner of the Issuer's securities indirectly held by NSSP as a Farallon Akubra Fund. The NSSP General Partner disclaims any beneficial ownership of any of the Issuer's securities reported or noted herein for purposes of Section 16 of the Securities Exchange Act of 1934, as amended (the &quot;'34 Act&quot;), or otherwise, except as to securities representing its pro rata interest in, and interest in the profits of, Akubra.</footnote>
        <footnote id="F3">As the manager of the NSSP General Partner, Farallon Capital Management, L.L.C. (the &quot;Management Company&quot;) may be deemed to be a beneficial owner of the Issuer's securities held by NSSP as a Farallon Akubra Fund. The Management Company disclaims any beneficial ownership of any of the Issuer's securities reported or noted herein for purposes of Section 16 of the '34 Act, or otherwise, except as to securities representing its pro rata interest in, and interest in the profits of, Akubra.</footnote>
        <footnote id="F4">The members of Bushranger are FCP XR 2014, L.L.C. (&quot;FCP XR&quot;), Farallon Capital Institutional Partners III, L.P. (&quot;FCIP III&quot;), and Farallon Capital AA Investors, L.P. (&quot;FCAAI&quot;) (collectively, the &quot;Farallon Bushranger Funds&quot;). As the general partner of FCAAI, Farallon AA GP, L.L.C. (the &quot;FCAAI General Partner&quot;) may be deemed to be a beneficial owner of the Issuer's securities indirectly held by FCAAI as a Farallon Bushranger Fund. The FCAAI General Partner disclaims any beneficial ownership of any of the Issuer's securities reported or noted herein for purposes of Section 16 of the '34 Act, or otherwise, except as to securities representing its pro rata interest in, and interest in the profits of, Bushranger.</footnote>
        <footnote id="F5">The members of Ute are FCOI II SS 2014, Ltd. (&quot;FCOI II SS&quot;), Farallon Capital Institutional Partners II, L.P. (&quot;FCIP II&quot;), and Farallon Special Situation Partners VI, L.P. (&quot;FSSP VI&quot;) (collectively, the &quot;Farallon Ute Funds&quot;). As the general partner of FSSP VI, Farallon Partners GP VI, L.L.C. (the &quot;FSSP VI General Partner&quot;) may be deemed to be a beneficial owner of the Issuer's securities indirectly held by FSSP VI as a Farallon Ute Fund. The FSSP VI General Partner disclaims any beneficial ownership of any of the Issuer's securities reported or noted herein for purposes of Section 16 of the '34 Act, or otherwise, except as to securities representing its pro rata interest in, and interest in the profits of, Ute.</footnote>
        <footnote id="F6">As the general partner of each of (a) the sole member of FCIP XR, (b) the sole member of FCP XR, (c) FCIP III, (d) the sole member of FCOI II SS and (e) FCIP II, Farallon Partners, L.L.C. (the &quot;Farallon General Partner&quot;) may be deemed to be a beneficial owner of the Issuer's securities indirectly held by FCIP XR as a Farallon Akubra Fund, FCP XR and FCIP III as Farallon Bushranger Funds, and FCOI II SS and FCIP II as Farallon Ute Funds. The Farallon General Partner disclaims any beneficial ownership of any of the Issuer's securities reported or noted herein for purposes of Section 16 of the '34 Act, or otherwise, except as to securities representing its pro rata interest in, and interest in the profits of, the Farallon SPVs.</footnote>
        <footnote id="F7">Hirsch, as a managing member of both the Farallon General Partner and the Management Company, and as a manager of both the FCAAI General Partner and the FSSP VI General Partner, in each case with the power to exercise investment discretion, may have been deemed to be a beneficial owner of the Issuer's securities held by the Farallon SPVs. Effective as of December 31, 2016, in connection with his resignation as a managing member of both the Farallon General Partner and the Management Company, and as a manager of both the FCAAI General Partner and the FSSP VI General Partner, Hirsch may no longer be deemed a beneficial owner of any of the Issuer's securities deemed beneficially owned by each of the Farallon General Partner, the Management Company, the FCAAI General Partner and the FSSP VI General Partner.</footnote>
        <footnote id="F8">Hirsch and the other individuals identified in the prior Form 3s and Form 4s filed by the foregoing disclaims any beneficial ownership of any of the Issuer's securities reported or referred to herein or therein for purposes of Section 16 of the '34 Act, or otherwise, except to the extent of his or her pecuniary interest, if any.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Monica R. Landry, as attorney-in-fact and/or authorized signer for Daniel J. Hirsch</signatureName>
        <signatureDate>2017-01-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
