A search for the decay BS0→K¯∗0μ+μ− is presented using data sets corresponding to 1.0, 2.0 and 1.6 fb−1 of integrated luminosity collected during pp collisions with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, respectively. An excess is found over the background-only hypothesis with a significance of 3.4 standard deviations. The branching fraction of the BS0→K¯∗0μ+μ− decay is determined to be ℬ(Bs0→K¯∗0μ+μ−)=[2.9±1.0(stat)±0.2(syst)±0.3(norm)]×10−8, where the first and second uncertainties are statistical and systematic, respectively. The third uncertainty is due to limited knowledge of external parameters used to normalise the branching fraction measurement.[Figure not available: see fulltext.].