© 2016, The Author(s). A measurement of the differential branching fraction of the decay B0 → K∗(892)0μ+μ− is presented together with a determination of the S-wave fraction of the K+π− system in the decay B0 → K+π−μ+μ−. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb−1 collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q2. Precise theoretical predictions for the differential branching fraction of B0 → K∗(892)0μ+μ− decays are available for the q2 region 1.1 < q2< 6.0 GeV2/c4. In this q2 region, for the K+π− invariant mass range 796 < mKπ< 996 MeV/c2, the S-wave fraction of the K+π− system in B0 → K+π−μ+μ− decays is found to be FS=0.101±0.017(stat)±0.009(syst), and the differential branching fraction of B0 → K∗(892)0μ+μ− decays is determined to be dℬ/dq2=(0.392−0.019+0.020(stat)±0.010(syst)±0.027(norm))×10−7c4/GeV2. The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.