The radiative hyperon decay Λ→nγ is studied using (10087±44)×10^{6} J/ψ events collected with the BESIII detector operating at BEPCII. The absolute branching fraction of the decay Λ→nγ is determined to be (0.832±0.038_{stat}±0.054_{syst})×10^{-3}, which is a factor of 2.1 lower and 5.6 standard deviations different than the previous measurement. By analyzing the joint angular distribution of the decay products, the first determination of the decay asymmetry α_{γ} is reported with a value of -0.16±0.10_{stat}±0.05_{syst}.