We explore supersymmetric contributions to the decay K_S^0→μ^+μ^-, in light of current experimental data. The Standard Model (SM) predicts B(K_S^0→μ^+μ^-)≈5× 10^-12. We find that contributions arising from flavour violating Higgs penguins can enhance the branching fraction up to ≈ 35× 10^-12 within different scenarios of the Minimal Supersymmetric Standard Model (MSSM), as well as suppress it down to ≈ 0.78× 10^-12. Regions with fine-tuned parameters can bring the branching fraction up to the

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... rrent experimental upper bound, 8× 10^-10. The mass degeneracy of the heavy Higgs bosons in MSSM induces correlations between B(K_S^0→μ^+μ^-) and B(K_L^0→μ^+μ^-). Predictions for the CP asymmetry in K^0→μ^+μ^- decays in the context of MSSM are also given, and can be up to eight times bigger than in the SM.