The first observation of the D^{0}→π^{+}π^{-}μ^{+}μ^{-} and D^{0}→K^{+}K^{-}μ^{+}μ^{-} decays is reported using a sample of proton-proton collisions collected by LHCb at a center-of-mass energy of 8 TeV, and corresponding to 2  fb^{-1} of integrated luminosity. The corresponding branching fractions are measured using as normalization the decay D^{0}→K^{-}π^{+}[μ^{+}μ^{-}]_{ρ^{0}/ω}, where the two muons are consistent with coming from the decay of a ρ^{0} or ω meson. The results are B(D^{0}→π^{+}π^{-}μ^{+}μ^{-})=(9.64±0.48±0.51±0.97)×10^{-7} and B(D^{0}→K^{+}K^{-}μ^{+}μ^{-})=(1.54±0.27±0.09±0.16)×10^{-7}, where the uncertainties are statistical, systematic, and due to the limited knowledge of the normalization branching fraction. The dependence of the branching fraction on the dimuon mass is also investigated.