The production of (2S) mesons is studied in dimuon final states using proton-lead (pPb) collision data collected by the LHCb detector. The data sample corresponds to an integrated luminosity of 1.6 nb1. The nucleon-nucleon centre-of-mass energy of the pPb collisions is sNN=5 TeV. The measurement is performed using (2S) mesons with transverse momentum less than 14 GeV/c and rapidity y in the ranges 1.5 < y < 4.0 and 5.0 < y < 2.5 in the nucleon-nucleon centre-of-mass system. The forward-backward production ratio and the nuclear modification factor are determined for (2S) mesons. Using the production cross-section results of (2S) and J/ mesons from b-hadron decays, the bb¯¯ cross-section in pPb collisions at sNN=5 TeV is obtained.