Two-loop contributions of flavor-changing neutral Higgs bosons to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mo>→</mml:mo><mml:mi>e</mml:mi><mml:mi>γ</mml:mi></mml:math>

The two-loop mechanism of Bjorken and Weinberg is used to constrain flavor-changing neutral Higgs bosons. We calculate the complete set of two-loop diagrams for the rare decay $\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma}$ induced by such neutral Higgs bosons, for arbitrary Higgs boson and top quark masses. The analytic result is used to set limits on Higgs boson masses for some recent models with a specific ansatz about the flavor-changing couplings. For example, in the Cheng-Sher scenario of multi-Higgs-doublet models, all neutral Higgs bosons possess flavor-changing (${f}_{i}\ensuremath{\leftrightarrow}{f}_{j}$) couplings proportional to $\sqrt{{m}_{i}{m}_{j}}$. We find that the present limit on $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ implies that, in such a scheme, these neutral Higgs bosons should be heavier than 200 GeV.