We report the first observation of a baryonic B_{s}^{0} decay, B_{s}^{0}→pΛ[over ¯]K^{-}, using proton-proton collision data recorded by the LHCb experiment at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb^{-1}. The branching fraction is measured to be B(B_{s}^{0}→pΛ[over ¯]K^{-})+B(B_{s}^{0}→p[over ¯]ΛK^{+})=[5.46±0.61±0.57±0.50(B)±0.32(f_{s}/f_{d})]×10^{-6}, where the first uncertainty is statistical and the second systematic, the third uncertainty accounts for the experimental uncertainty on the branching fraction of the B^{0}→pΛ[over ¯]π^{-} decay used for normalization, and the fourth uncertainty relates to the knowledge of the ratio of b-quark hadronization probabilities f_{s}/f_{d}.