The differential cross-section for the inclusive production of ψ(2S) mesons in pp collisions at √s = 7 TeV has been measured with the LHCb detector. The data sample corresponds to an integrated luminosity of 36 pb−1. The ψ(2S) mesons are reconstructed in the decay channels ψ(2S) → μ+μ− and ψ(2S) → J/ψπ+π−, with the J/ψ meson decaying into two muons. Results are presented both for promptly produced ψ(2S) mesons and for those originating from b-hadron decays. In the kinematic range pT(ψ(2S)) ≤ 16 GeV/c and 2 < y(ψ(2S)) ≤ 4.5 we measure σprompt ψ(2S) = 1.44 ± 0.01 (stat) ± 0.12 (syst) +0.20 −0.40 (pol) µb, σb ψ(2S) = 0.25 ± 0.01 (stat) ± 0.02 (syst) µb, where the last uncertainty on the prompt cross-section is due to the unknown ψ(2S) polarization. Recent QCD calculations are found to be in good agreement with our measurements. Combining the present result with the LHCb J/ψ measurements we determine the inclusive branching fraction B b → ψ(2S)X = 2.73 ± 0.06 (stat) ± 0.16 (syst) ± 0.24 (BF) × 10−3, where the last uncertainty is due to the B(b → J/ψX), B(J/ψ → μ+μ−) and B(ψ(2S) → e+e−) branching fraction uncertainties.