The first observation of the decay Ξ− b → ψ(2S)Ξ− and measurement of the branching ratio of Ξ− b → ψ(2S)Ξ− to Ξ− b → J/ψΞ− are presented. The J/ψ and ψ(2S) mesons are reconstructed using their dimuon decay modes. The results are based on proton-proton colliding beam data from the LHC collected by the CMS experiment at √s = 13 TeV in 2016–2018, corresponding to an integrated luminosity of 140 fb−1. The branching fraction ratio is measured to be B(Ξ− b → ψ(2S)Ξ−)/B(Ξ− b → J/ψΞ−) = 0.84+0.21 −0.19 (stat) ± 0.10(syst) ± 0.02(B), where the last uncertainty comes from the uncertainties in the branching fractions of the charmonium states. New measurements of the Ξb(5945)0 baryon mass and natural width are also presented, using the Ξ− bπ+ final state, where the Ξ− b baryon is reconstructed through the decays J/ψΞ−, ψ(2S)Ξ−, J/ψΛK−, and J/ψΣ0K−. Finally, the fraction of Ξ− b baryons produced from Ξb(5945)0 decays is determined.