The Ξ_{b}^{-}π^{+}π^{-} invariant mass spectrum is investigated with an event sample of proton-proton collisions at sqrt[s]=13 TeV, collected by the CMS experiment at the LHC in 2016-2018 and corresponding to an integrated luminosity of 140 fb^{-1}. The ground state Ξ_{b}^{-} is reconstructed via its decays to J/ψΞ^{-} and J/ψΛK^{-}. A narrow resonance, labeled Ξ_{b}(6100)^{-}, is observed at a Ξ_{b}^{-}π^{+}π^{-} invariant mass of 6100.3±0.2(stat)±0.1(syst)±0.6(Ξ_{b}^{-}) MeV, where the last uncertainty reflects the precision of the Ξ_{b}^{-} baryon mass. The upper limit on the Ξ_{b}(6100)^{-} natural width is determined to be 1.9 MeV at 95% confidence level. The low Ξ_{b}(6100)^{-} signal yield observed in data does not allow a measurement of the quantum numbers of the new state. However, following analogies with the established excited Ξ_{c} baryon states, the new Ξ_{b}(6100)^{-} resonance and its decay sequence are consistent with the orbitally excited Ξ_{b}^{-} baryon, with spin and parity quantum numbers J^{P}=3/2^{-}.