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We present the first observation of the Zγ → ννγ process at the Fermilab Tevatron at 5.1 standard deviations significance, based on 3.6 fb-1 of integrated luminosity collected with the D0 detector at the Fermilab Tevatron pp Collider at √s = 1.96 TeV. The measured Zγ production cross section multiplied by the branching fraction of Z → νν is 32 ± 9(stat + syst) ± 2(lumi) fb for the photon ET > 90 GeV. It is in agreement with the standard model prediction of 39 ± 4 fb. We set limits on anomalous trilinear Zγγ and ZZγ gauge boson couplings, most of which are the most restrictive to date.