Production of mesons in proton-lead collisions at a nucleon-nucleon centre-of-mass energy = 5 TeV is studied with the LHCb detector. The analysis is based on a data sample corresponding to an integrated luminosity of 1.6 nb(-1). The mesons of transverse momenta up to 15 GeV/c are reconstructed in the dimuon decay mode. The rapidity coverage in the centre-of-mass system is 1.5 < y < 4.0 (forward region) and -5.0 < y < -2.5 (backward region). The forward-backward production ratio and the nuclear modification factor for (1S) mesons are determined. The data are compatible with the predictions for a suppression of (1S) production with respect to proton-proton collisions in the forward region, and an enhancement in the backward region. The suppression is found to be smaller than in the case of prompt J/psi mesons.