We have measured the differential cross section for the inclusive production of ψ(2S) mesons decaying to μ+μ− that were produced in prompt or B-decay processes from pp collisions at 1.96 TeV. These measurements have been made using a data set from an integrated luminosity of 1.1  fb−1 collected by the CDF II detector at Fermilab. For events with transverse momentum pT(ψ(2S))>2  GeV/c and rapidity |y(ψ(2S))|<0.6 we measure the integrated inclusive cross section σ(pp→ψ(2S)X)⋅Br(ψ(2S)→μ+μ−) to be 3.29±0.04(stat)±0.32(syst)  nb.