Extending the Minimal Supersymmetric Standard Model with three right-handed neutrino superfields is one of the best motivated scenarios for physics beyond the Standard Model. However, very little is known from observations about the high energy parameters of this model. In this paper we show, under the plausible assumptions that the neutrino Yukawa eigenvalues are hierarchical and the absence of cancellations, that there exists an upper bound on the smallest Yukawa eigenvalue stemming from the non-observation of the rare lepton decay μ→eγ. Furthermore, we show that this bound implies an upper bound on the lightest right-handed neutrino mass of approximately 5 × 10¹² GeV for typical supersymmetric parameters. We also discuss the implications of this upper bound for the minimal leptogenesis scenario based on the decay of the lightest right-handed neutrino and we argue that an improvement of sensitivity of six orders of magnitude to the process μ→eγ could rule out this mechanism as the origin of the observed baryon asymmetry, unless the neutrino parameters take very specific values.