A search for the decays of the Higgs and Z bosons to a φ meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of 2.7 fb-1 collected at s=13 TeV with the ATLAS detector at the LHC. No significant excess of events is observed above the background, and 95% confidence level upper limits on the branching fractions of the Higgs and Z boson decays to φγ of 1.4×10-3 and 8.3×10-6, respectively, are obtained.