A study of the decay $D^{0}\rightarrow K^{-}π^{+}μ^{+}μ^{-}$ 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$/c^2$ are considered. This region is dominated by the $ρ^{0}$ and $ω$ resonances. The branching fraction in this range is measured to be ${\cal B}$($D^{0}\rightarrow K^{-}π^{+}μ^{+}μ^{-}$) = $(4.17 \pm 0.12(stat) \pm 0.40(syst))\times10^{-6}$. This is the first observation of the decay $D^{0}\rightarrow K^{-}π^{+}μ^{+}μ^{-}$. Its branching fraction is consistent with the value expected in the Standard Model.