Using an e^{+}e^{-} collision data sample of 2.93 fb^{-1} collected at a center-of-mass energy of 3.773 GeV by the BESIII detector at BEPCII, we report the observation of D^{0}→a_{0}(980)^{-}e^{+}ν_{e} and evidence for D^{+}→a_{0}(980)^{0}e^{+}ν_{e} with significances of 6.4σ and 2.9σ, respectively. The absolute branching fractions are determined to be B(D^{0}→a_{0}(980)^{-}e^{+}ν_{e})×B(a_{0}(980)^{-}→ηπ^{-})=[1.33_{-0.29}^{+0.33}(stat)±0.09(syst)]×10^{-4} and B(D^{+}→a_{0}(980)^{0}e^{+}ν_{e})×B(a_{0}(980)^{0}→ηπ^{0})=[1.66_{-0.66}^{+0.81}(stat)±0.11(syst)]×10^{-4}. This is the first time the a_{0}(980) meson has been measured in a D^{0} semileptonic decay, which would open one more interesting page in the investigation of the nature of the puzzling a_{0}(980) states.