Measurements of prompt ψ(2S) meson production cross sections in proton–lead (pPb) and proton–proton (pp) collisions at a nucleon–nucleon center-of-mass energy of sNN=5.02TeV are reported. The results are based on pPb and pp data collected by the CMS experiment at the LHC, corresponding to integrated luminosities of 34.6nb−1 and 28.0pb−1 , respectively. The nuclear modification factor RpPb is measured for prompt ψ(2S) in the transverse momentum range 4<pT<30GeV/c and the center-of-mass rapidity range −2.4<yCM<1.93. The results on ψ(2S) RpPb are compared to the corresponding modification factor for prompt J/ψ mesons. The results point to different nuclear effects at play in the production of the excited charmonium state compared to the ground state, in the region of backward rapidity and for pT<10GeV/c.