Results on the production of the double strange cascade hyperon Ξ^{-} are reported for collisions of p(3.5 GeV)+Nb, studied with the High Acceptance Di-Electron Spectrometer (HADES) at SIS18 at GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt. For the first time, subthreshold Ξ^{-} production is observed in proton-nucleus interactions. Assuming a Ξ^{-} phase-space distribution similar to that of Λ hyperons, the production probability amounts to P_{Ξ^{-}}=[2.0±0.4(stat)±0.3(norm)±0.6(syst)]×10^{-4} resulting in a Ξ^{-}/(Λ+Σ^{0}) ratio of P_{Ξ^{-}}/P_{Λ+Σ^{0}}=[1.2±0.3(stat)±0.4(syst)]×10^{-2}. Available model predictions are significantly lower than the measured Ξ^{-} yield.