Using e^{+}e^{-} annihilation data of 2.93 fb^{-1} collected at center-of-mass energy sqrt[s]=3.773 GeV with the BESIII detector, we measure the absolute branching fraction of D^{0}→K^{-}μ^{+}ν_{μ} with significantly improved precision: B_{D^{0}→K^{-}μ^{+}ν_{μ}}=(3.413±0.019_{stat}±0.035_{syst})%. Combining with our previous measurement of B_{D^{0}→K^{-}e^{+}ν_{e}}, the ratio of the two branching fractions is determined to be B_{D^{0}→K^{-}μ^{+}ν_{μ}}/B_{D^{0}→K^{-}e^{+}ν_{e}}=0.974±0.007_{stat}±0.012_{syst}, which agrees with the theoretical expectation of lepton flavor universality within the uncertainty. A study of the ratio of the two branching fractions in different four-momentum transfer regions is also performed, and no evidence for lepton flavor universality violation is found with current statistics. Taking inputs from global fit in the standard model and lattice quantum chromodynamics separately, we determine f_{+}^{K}(0)=0.7327±0.0039_{stat}±0.0030_{syst} and |V_{cs}|=0.955±0.005_{stat}±0.004_{syst}±0.024_{LQCD}.