A search is presented for decays of Z and Higgs bosons to a J / ψ meson and a photon, with the subsequent decay of the J / ψ to μ + μ - . The analysis uses data from proton-proton collisions with an integrated luminosity of 35.9 fb - 1 at s = 13 TeV collected with the CMS detector at the LHC. The observed limit on the Z → J / ψ γ decay branching fraction, assuming that the J / ψ meson is produced unpolarized, is 1.4 × 10 - 6 at 95% confidence level, which corresponds to a rate higher than expected in the standard model by a factor of 15. For extreme-polarization scenarios, the observed limit changes from - 13.6 to + 8.6 % with respect to the unpolarized scenario. The observed upper limit on the branching fraction for H → J / ψ γ where the J / ψ meson is assumed to be transversely polarized is 7.6 × 10 - 4 , a factor of 260 larger than the standard model prediction. The results for the Higgs boson are combined with previous data from proton-proton collisions at s = 8 TeV to produce an observed upper limit on the branching fraction for H → J / ψ γ that is a factor of 220 larger than the standard model value.