We explore realizations of minimal flavor violation (MFV) for leptons in the simplest seesaw models where the neutrino mass generation mechanism is driven by new fermion singlets (type I) or triplets (type III) and by a scalar triplet (type II). We also discuss similarities and differences of the MFV implementation among the three scenarios. To study the phenomenological implications, we consider a number of effective dimension-six operators that are purely leptonic or couple leptons to the standard-model gauge and Higgs bosons and evaluate constraints on the scale of MFV associated with these operators from the latest experimental information. Specifically, we employ the most recent measurements of neutrino mixing parameters as well as the currently available data on flavor-violating radiative and three-body decays of charged leptons, mu -> e conversion in nuclei, the anomalous magnetic moments of charged leptons, and their electric dipole moments. The most stringent lower-limit on the MFV scale comes from the present experimental bound on mu -> e gamma and can reach 500 TeV or higher, depending on the details of the seesaw scheme. With our numerical results, we illustrate some important differences among the seesaw types. In particular, we show that in types I and III there are features which can bring about potentially remarkable effects which do not occur in type II. In addition, we comment on how one of the new effective operators can induce flavor-changing dilepton decays of the Higgs boson, which may be probed in upcoming searches at the LHC.