Production of π0 and η mesons has been measured at midrapidity in Cu+Au collisions at √sNN = 200 GeV. Measurements were performed in π0 (η) → γ γ decay channel in the 1(2)-20 GeV/c transverse momentum range. A strong suppression is observed for π0 and η meson production at high transverse momentum in central Cu+Au collisions relative to the p + p results scaled by the number of nucleon-nucleon collisions. In central collisions the suppression is similar to Au + Au with comparable nuclear overlap. The η/π0 ratio measured as a function of transverse momentum is consistent with mT -scaling parametrization down to pT = 2 GeV/c, its asymptotic value is constant and consistent with Au + Au and p + p and does not show any significant dependence on collision centrality. Similar results were obtained in hadron-hadron, hadron-nucleus, and nucleusnucleus collisions as well as in e+e− collisions in a range of collision energies √sNN = 3−1800 GeV. This suggests that the quark-gluon-plasma medium produced in Cu+Cu collisions either does not affect the jet fragmentation into light mesons or it affects the π0 and η the same way.