Results of a search for physics beyond the Standard Model in events containing an energetic photon and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. As the number of events observed in data, corresponding to an integrated luminosity of 36.1 fb[Formula: see text] of proton-proton collisions at a centre-of-mass energy of [Formula: see text], is in agreement with the Standard Model expectations, model-independent limits are set on the fiducial cross section for the production of events in this final state. Exclusion limits are also placed in models where dark-matter candidates are pair-produced. For dark-matter production via an axial-vector or a vector mediator in the s-channel, this search excludes mediator masses below 750-[Formula: see text] for dark-matter candidate masses below 230-[Formula: see text] at 95% confidence level, depending on the couplings. In an effective theory of dark-matter production, the limits restrict the value of the suppression scale [Formula: see text] to be above [Formula: see text] at 95% confidence level. A limit is also reported on the production of a high-mass scalar resonance by processes beyond the Standard Model, in which the resonance decays to [Formula: see text] and the Z boson subsequently decays into neutrinos.