We study constraints and implications of the recent LHCb measurement of ${cal B}(B_s to mu^+mu^-)$ for tree-level Higgs-mediated flavor-changing neutral current (FCNC) interactions. Combined with experimental data on $B_s$ mass difference $Delta m_s$, the $h to mu tau$, and the $h to tau^+tau^-$ decay branching ratios from the LHC, we find that the Higgs FCNC couplings are severely constrained. The allowed regions for $B_s to mu tau$, $tautau$ and $h to sb$ decays are obtained. Current data allow large CP violation in the $h to tau^+ tau^-$ decay. Consequences of the Cheng-Sher ansatz for the Higgs Yukawa couplings are discussed in some detail.
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