.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/c2 are considered. This region is dominated by the ρ0 and ω resonances. The branching fraction in this range is measured to B(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
