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 36.1 fb−1 collected by the ATLAS detector in 2015 and 2016. Zγ events with invisible decays of the Z boson are selected by requiring significant missing transverse energy (EmissT) in conjunction with a single isolated photon with large transverse energy (ET). The rate of Zγ production is measured as a function of photon ET, EmissT and jet multiplicity. Evidence for anomalous triple gauge coupling is sought in Zγ production with photon ET 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.