The decay B+c→ψ(2S)π+ with ψ(2S)→μ+μ− is observed with a significance of 5.2σ using pp collision data corresponding to an integrated luminosity of 1.0  fb−1 collected by the LHCb experiment. The branching fraction of B+c→ψ(2S)π+ decays relative to that of the B+c→J/ψπ+ mode is measured to be B(B+c→ψ(2S)π+)B(B+c→J/ψπ+)=0.250±0.068(stat)±0.014(syst)±0.006(B). The last term is the uncertainty on the ratio B(ψ(2S)→μ+μ−)/B(J/ψ→μ+μ−).