Using a data sample corresponding to an integrated luminosity of 2.93 fb^{-1} taken at a center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider, we perform an analysis of the semileptonic decays D^{0(+)}→π^{-(0)}μ^{+}ν_{μ}. The branching fractions of D^{0}→π^{-}μ^{+}ν_{μ} and D^{+}→π^{0}μ^{+}ν_{μ} are measured to be (0.272±0.008_{stat}±0.006_{syst})% and (0.350±0.011_{stat}±0.010_{syst})%, respectively, where the former is of much improved precision compared to previous results and the latter is determined for the first time. Using these results along with previous BESIII measurements of D^{0(+)}→π^{-(0)}e^{+}ν_{e}, we calculate the branching fraction ratios to be R^{0}≡B_{D^{0}→π^{-}μ^{+}ν_{μ}}/B_{D^{0}→π^{-}e^{+}ν_{e}}=0.922±0.030_{stat}±0.022_{syst} and R^{+}≡B_{D^{+}→π^{0}μ^{+}ν_{μ}}/B_{D^{+}→π^{0}e^{+}ν_{e}}=0.964±0.037_{stat}±0.026_{syst}, which are compatible with the theoretical expectation of lepton flavor universality within 1.7σ and 0.5σ, respectively. We also examine the branching fraction ratios in different four-momentum transfer square regions, and find no significant deviations from the standard model predictions.