By analyzing a 2.93 fb^{-1} data sample of e^{+}e^{-} collisions, recorded at a center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider, we report the first observation of the semileptonic D^{+} transition into the axial-vector meson D^{+}→K[over ¯]_{1}(1270)^{0}e^{+}ν_{e} with a statistical significance greater than 10σ. Its decay branching fraction is determined to be B[D^{+}→K[over ¯]_{1}(1270)^{0}e^{+}ν_{e}]=(2.30±0.26_{-0.21}^{+0.18}±0.25)×10^{-3}, where the first and second uncertainties are statistical and systematic, respectively, and the third originates from the input branching fraction of K[over ¯]_{1}(1270)^{0}→K^{-}π^{+}π^{0}.