  We explore supersymmetric contributions to the decay
$K_S^0\rightarrow\mu^+\mu^-$, in light of current experimental data. The
Standard Model (SM) predicts
$\mathcal{B}(K_S^0\rightarrow\mu^+\mu^-)\approx5\times 10^{-12}$. We find that
contributions arising from flavour violating Higgs penguins can enhance the
branching fraction up to $\approx 35\times 10^{-12}$ within different scenarios
of the Minimal Supersymmetric Standard Model (MSSM), as well as suppress it
down to $\approx 0.78\times 10^{-12}$. Regions with fine-tuned parameters can
bring the branching fraction up to the current experimental upper bound,
$8\times 10^{-10}$. The mass degeneracy of the heavy Higgs bosons in MSSM
induces correlations between $\mathcal{B}(K_S^0\rightarrow\mu^+\mu^-)$ and
$\mathcal{B}(K_L^0\rightarrow\mu^+\mu^-)$. Predictions for the $CP$ asymmetry
in $K^0\rightarrow\mu^+\mu^-$ decays in the context of MSSM are also given, and
can be up to eight times bigger than in the SM.
