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)→γγ 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 nucleus-nucleus 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.