A measurement of the flavor-untagged decay-time-integrated CP asymmetry in the flavor-specific decay B_{s}^{0}→D_{s}^{-}π^{+}, ⟨A_{untagged}^{s}⟩, is performed using proton-proton collision data collected by the LHCb experiment between 2016 and 2018 at a center-of-mass energy of 13 TeV, corresponding to a total integrated luminosity of 5.4 fb^{-1}. The CP asymmetry is measured in two D_{s}^{-} meson decay modes, D_{s}^{-}→K^{-}K^{+}π^{-} and D_{s}^{-}→π^{-}π^{+}π^{-}. The combined result, ⟨A_{untagged}^{s}⟩=(-1.4±5.9(stat)±1.1(syst))×10^{-3}, is consistent with the Standard Model expectation and provides a direct constraint on new physics in tree-level b-hadron decays.