An observation of the Λ_b ⁰→ψ(2S)Λ⁰ decay and a comparison of its branching fraction with that of the Λ_b ⁰→J/ψΛ⁰ decay has been made with the ATLAS detector in proton-proton collisions at s=8 TeV at the LHC using an integrated luminosity of 20.6 fb^-1. The J/ψ and ψ(2S) mesons are reconstructed in their decays to a muon pair, while the Λ⁰→ pπ^- decay is exploited for the Λ⁰ baryon reconstruction. The Λ_b ⁰ baryons are reconstructed with transverse momentum p_T>10 GeV and pseudorapidity |η|<2.1. The measured branching ratio of the Λ_b ⁰→ψ(2S)Λ⁰ and Λ_b ⁰J/ψΛ⁰ decays is G{cyrillic}(Λ_b ⁰→ψ(2S)Λ⁰/G{cyrillic}(Λ_b ⁰J/ψΛ⁰)=0.501±0.033(stat)±0.019(syst), lower than the expectation from the covariant quark model.