We consider a supersymmetric version of the inert Higgs doublet model, whose motivation is to explain smallness of neutrino masses and existence of dark matter. In this supersymmetric model, due to the presence of discrete symmetries, neutrinos acquire masses at loop level. After computing these neutrino masses, in order to fit the neutrino oscillation data, we show that by tuning some supersymmetry-breaking soft parameters of the model, neutrino Yukawa couplings can be unsuppressed. In the above-mentioned parameter space, we compute the branching ratio of the decay μ→eγ. To be consistent with the current experimental upper bound on Br(μ→eγ), we obtain constraints on the right-handed neutrino mass of this model. © 2016 American Physical Society.