© 2018, The Author(s). The production of Z bosons in association with a high-energy photon (Zγ production) is studied in the neutrino decay channel of the Z boson using pp collisions at s=13 TeV. The analysis uses a data sample with an integrated luminosity of 36.1fb −1 collected by the ATLAS detector at the LHC in 2015 and 2016. Candidate Zγ events with invisible decays of the Z boson are selected by requiring significant transverse momentum (p T ) of the dineutrino system in conjunction with a single isolated photon with large transverse energy (E T ). The rate of Zγ production is measured as a function of photon E T , dineutrino system p T and jet multiplicity. Evidence of anomalous triple gauge-boson couplings is sought in Zγ production with photon E T greater than 600 GeV. No excess is observed relative to the Standard Model expectation, and upper limits are set on the strength of ZZγ and Zγγ couplings.[Figure not available: see fulltext.].