The angular distributions and the partial branching fraction of the decay B0→K*0μ+μ− are studied by using an integrated luminosity of 0.37  fb−1 of data collected with the LHCb detector. The forward-backward asymmetry of the muons, AFB, the fraction of longitudinal polarization, FL, and the partial branching fraction dB/dq2 are determined as a function of the dimuon invariant mass. The measurements are in good agreement with the standard model predictions and are the most precise to date. In the dimuon invariant mass squared range 1.00–6.00  GeV2/c4, the results are AFB=−0.06+0.13−0.14±0.04, FL=0.55±0.10±0.03, and dB/dq2=(0.42±0.06±0.03)×10−7  c4/GeV2. In each case, the first error is statistical and the second systematic.