We calculate the two-loop diagrams that give a nonzero contribution to the electric dipole moment d(l) of a charged lepton l due to possible Majorana masses of neutrinos. Using the example with one generation of the standard model leptons and two heavy right-handed neutrinos, we demonstrate that the nonvanishing result for d(l) first appears in order O(m(l)m(nu)(2)G(F)(2)), where m(nu) is the mass of the light neutrino and the see-saw type relation is imposed. This effect is beyond the reach of presently planned experiments.