Neutral pion and η meson invariant differential yields were measured in non-single diffractive p–Pb collisions at sNN = 5.02 TeV with the ALICE experiment at the CERN LHC. The analysis combines results from three complementary photon measurements, utilizing the PHOS and EMCal calorimeters and the Photon Conversion Method. The invariant differential yields of π⁰ and η meson inclusive production are measured near mid-rapidity in a broad transverse momentum range of 0.3<pT<20GeV/c and 0.7<pT<20GeV/c, respectively. The measured η/ π⁰ ratio increases with p_T and saturates for p_T > 4 GeV / c at 0.483 ± 0. 015 _stat± 0. 015 _sys. A deviation from m_T scaling is observed for p_T< 2 GeV / c. The measured η/ π⁰ ratio is consistent with previous measurements from proton-nucleus and pp collisions over the full p_T range. The measured η/ π⁰ ratio at high p_T also agrees within uncertainties with measurements from nucleus–nucleus collisions. The π⁰ and η yields in p–Pb relative to the scaled pp interpolated reference, R_pPb, are presented for 0.3 < p_T< 20 GeV / c and 0.7 < p_T< 20 GeV / c, respectively. The results are compared with theoretical model calculations. The values of R_pPb are consistent with unity for transverse momenta above 2 GeV / c. These results support the interpretation that the suppressed yield of neutral mesons measured in Pb–Pb collisions at LHC energies is due to parton energy loss in the hot QCD medium.