Using a data sample corresponding to an integrated luminosity of 2.93 fb^{-1} collected at a center-of-mass energy sqrt[s]=3.773 GeV by the BESIII detector, the decay D^{0}→ωϕ is observed for the first time. The branching fraction is measured to be (6.48±0.96±0.40)×10^{-4} with a significance of 6.3σ, where the first and second uncertainties are statistical and systematic, respectively. An angular analysis reveals that the ϕ and ω mesons from the D^{0}→ωϕ decay are transversely polarized. The 95% confidence level upper limit on longitudinal polarization fraction is set to be less than 0.24, which is inconsistent with current theoretical expectations and challenges our understanding of the underlying dynamics in charm meson decays.