A search for the decay $${{K} ^0_{\mathrm { \scriptscriptstyle S}}} \rightarrow \mu ^+\mu ^-$$ is performed, based on a data sample of proton-proton collisions corresponding to an integrated luminosity of $$3\,\text{ fb }^{-1} $$ , collected by the LHCb experiment at centre-of-mass energies of 7 and 8 $$\mathrm {\,TeV}$$ . The observed yield is consistent with the background-only hypothesis, yielding a limit on the branching fraction of $$\mathcal{B}({{K} ^0_{\mathrm { \scriptscriptstyle S}}} \rightarrow \mu ^+\mu ^-) < 0.8~(1.0) \times 10^{-9}$$ at $$90\%~(95\%)$$ confidence level. This result improves the previous upper limit on the branching fraction by an order of magnitude.