The production of psi(2S) mesons in proton-lead collisions at a centre-of-mass energy per nucleon pair of root s(NN) = 8.16TeV is studied with the LHCb detector using data corresponding to an integrated luminosity of 34 nb(-1). The prompt and nonprompt psi(2S) production cross-sections and the ratio of the psi(2S) to J/psi cross-section are measured as a function of the meson transverse momentum and rapidity in the nucleon-nucleon centre-of-mass frame, together with forward-to-backward ratios and nuclear modification factors. The production of prompt psi(2S) is observed to be more suppressed compared to pp collisions than the prompt J/psi production, while the nonprompt productions have similar suppression factors.