  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 $D^0 \to\omega\phi$ is observed for the first time.
The branching fraction is measured to be $(6.48 \pm 0.96 \pm 0.40)\times
10^{-4}$ with a significance of $6.3 \sigma$, where the first and second
uncertainties are statistical and systematic, respectively. An angular analysis
reveals that the $\phi$ and $\omega$ mesons from the $D^0 \to \omega \phi$
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.
