  The production of $Z$ bosons in association with a high-energy photon
($Z\gamma$ production) is studied in the neutrino decay channel of the $Z$
boson using $pp$ collisions at $\sqrt{s}$ = 13 TeV. The analysis uses a data
sample with an integrated luminosity of 36.1 fb$^{-1}$ collected by the ATLAS
detector at the LHC in 2015 and 2016. Candidate $Z\gamma$ 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 $Z\gamma$
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 $Z\gamma$ 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 $ZZ\gamma$ and $Z\gamma\gamma$
couplings.
