The singly Cabibbo-suppressed decay Λ_{c}^{+}→nπ^{+} is observed for the first time with a statistical significance of 7.3σ by using 3.9 fb^{-1} of e^{+}e^{-} collision data collected at center-of-mass energies between 4.612 and 4.699 GeV with the BESIII detector at BEPCII. The branching fraction of Λ_{c}^{+}→nπ^{+} is measured to be (6.6±1.2_{stat}±0.4_{syst})×10^{-4}. By taking the upper limit of branching fractions of Λ_{c}^{+}→pπ^{0} from the Belle experiment, the ratio of branching fractions between Λ_{c}^{+}→nπ^{+} and Λ_{c}^{+}→pπ^{0} is calculated to be larger than 7.2 at the 90% confidence level, which disagrees with most predictions of the available phenomenological models. In addition, the branching fractions of the Cabibbo-favored decays Λ_{c}^{+}→Λπ^{+} and Λ_{c}^{+}→Σ^{0}π^{+} are measured to be (1.31±0.08_{stat}±0.05_{syst})×10^{-2} and (1.22±0.08_{stat}±0.07_{syst})×10^{-2}, respectively, which are consistent with previous results.