The absolute branching fraction of Λ→pμ^{-}ν[over ¯]_{μ} is reported for the first time based on an e^{+}e^{-} annihilation sample of 10×10^{9} J/ψ events collected with the BESIII detector at sqrt[s]=3.097 GeV. The branching fraction is determined to be B(Λ→pμ^{-}ν[over ¯]_{μ})=[1.48±0.21(stat)±0.08(syst)]×10^{-4}, which is improved by about 30% in precision over the previous indirect measurements. Combining this result with the world average of B(Λ→pe^{-}ν[over ¯]_{e}), we obtain the ratio {[Γ(Λ→pμ^{-}ν[over ¯]_{μ})]/[Γ(Λ→pe^{-}ν[over ¯]_{e})]} to be 0.178±0.028, which agrees with the standard model prediction assuming lepton flavor universality. The asymmetry of the branching fractions of Λ→pμ^{-}ν[over ¯]_{μ} and Λ[over ¯]→p[over ¯]μ^{+}ν_{μ} is also determined, and no evidence for CP violation is found.