  A study of the decay $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$ 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
$\rho^{0}$ and $\omega$ resonances. The branching fraction in this range is
measured to be ${\cal B}$($D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$) =
$(4.17 \pm 0.12(stat) \pm 0.40(syst))\times10^{-6}$. This is the first
observation of the decay $D^{0}\rightarrow K^{-}\pi^{+}\mu^{+}\mu^{-}$. Its
branching fraction is consistent with the value expected in the Standard Model.
