  We consider the tentative indication of flavor-violating Higgs boson decay
$h\to\mu\tau$ recently reported in the CMS experiment within the framework of
minimal flavor violation. Specifically, we adopt the standard model extended
with the seesaw mechanism involving right-handed neutrinos plus effective
dimension-six operators satisfying the minimal flavor violation principle in
the lepton sector. We find that it is possible to accommodate the CMS
$h\to\mu\tau$ signal interpretation provided that the right-handed neutrinos
couple to the Higgs boson in some nontrivial way. We take into account
empirical constraints from other lepton-flavor-violating processes and discuss
how future searches for the $\mu\to e\gamma$ decay and $\mu\to e$ conversion in
nuclei may further probe the lepton-flavor-violating Higgs couplings.
