A search for the decays of the Higgs and Z bosons to a phi meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of 2.7 fb(-1) collected at root 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 phi gamma of 1.4 x 10(-3) and 8.3 x 10(-6), respectively, are obtained.