We report on a calculation of Higgs-boson contributions to the decays B s → l + l − andB → Kl + l − (l = e, µ) which are governed by the effective Hamiltonian describing b → sl + 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 β. We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including b → sγ,B s → µ + µ − , andB → K ( * ) µ + µ − . In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio ofB s → µ + µ − and the forward-backward (FB) asymmetry of µ − inB → Kµ + µ − decay. 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 6 × 10 −7 . Moreover, striking effects on the decay spectrum ofB → Kµ + µ − are already ruled out by experimental data on theB s → µ + µ − 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 → sγ can significantly affect the branching ratio ofB s → µ + µ − . We also comment on previous calculations *