  We report on a calculation of Higgs-boson contributions to the decays B_s ->
l^+l^- and B -> K l^+l^- (l=e, mu) which are governed by the effective
Hamiltonian describing b -> s l^+ l^-. Compact formulae for the Wilson
coefficients are provided in the context of the type-II two-Higgs-doublet model
(2HDM) and supersymmetry (SUSY) with minimal flavour violation, focusing on the
case of large tan(beta). We derive, in a model-independent way, constraints on
Higgs-boson-mediated interactions, using present experimental results on rare B
decays including b -> s gamma, B_s -> mu^+ mu^-, and B -> K^(*) mu^+ mu^-. In
particular, we assess the impact of possible scalar and pseudoscalar
interactions transcending the standard model (SM) on the branching ratio of B_s
-> mu^+ mu^- and the forward-backward (FB) asymmetry of mu^- in B -> K mu^+
mu^- decay. We find that the average FB asymmetry, which is unobservably small
within the SM, and therefore a potentially valuable tool to search for new
physics, is predicted to be no greater than 4% for a nominal branching ratio of
about 6x10^{-7}. Moreover, striking effects on the decay spectrum of B -> K
mu^+ mu^- are already ruled out by experimental data on the B_s -> mu^+ mu^-
branching fraction. In addition, we study the constraints on the parameter
space of the 2HDM and SUSY with minimal flavour violation. While the type-II
2HDM does not give any sizable contributions to the above decay modes, we find
that SUSY contributions obeying the constraint on b -> s gamma can affect
significantly the branching ratio of B_s -> mu^+ mu^-. We also comment on
previous calculations contained in the literature.
