A study of the decay D0→K-π+μ+μ-is performed using data collected by the LHCb detector in proton-proton collisions at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2.0 fb-1. Decay candidates with muon pairs that have an invariant mass in the range 675-875 MeV/c2are considered. This region is dominated by the ρ0and ω resonances. The branching fraction in this range is measured to beB(D0→K-π+μ+μ-)=(4.17±0.12(stat)±0.40(syst))×10-6. This is the first observation of the decay D0→K-π+μ+μ-. Its branching fraction is consistent with the value expected in the Standard Model.