  We derive novel limits on the masses of the light and heavy Majorana
neutrinos by requiring successful leptogenesis in seesaw models of minimal
flavour violation (MFV). Taking properly into account radiative flavour effects
and avoiding the limitations due to a no-go theorem on leptonic asymmetries, we
find that the mass of the lightest of the observable neutrinos must be smaller
than $\sim 0.05$ eV, whilst the Majorana scale of lepton number violation
should be higher than $\sim 10^{12}$ GeV. The latter lower bound enables one to
probe the existence of possible new scales of MFV, up to energies of $\sim 100$
TeV, in low-energy experiments, such as $\mu \to e\gamma$ and $\mu \to e$
conversion in nuclei. Possible realizations of MFV leptogenesis in Grand
Unified Theories are briefly discussed.
