By analyzing a sample of 20.3 fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at the center-of-mass energy of 3.773~GeV with the BESIII detector, we have made a first measurement of the absolute branching fractions of the radiative decays $D^0\to \gamma {\bar{K}}^{*0}$ and $D^0\to \gamma \varphi$ to be $(3.81 \pm 0.18_{\rm stat.} \pm 0.20_{\rm syst.})\times 10^{-4}$ and $(2.51 \pm 0.44_{\rm stat.} \pm 0.11_{\rm syst.})\times 10^{-5}$, respectively. The statistical significances of $D^0\to \gamma {\bar{K}}^{*0}$ and $D^0\to \gamma \varphi$ are $26.8\sigma$ and $7.9\sigma$, respectively. The obtained branching fractions are consistent with the corresponding world average values. In addition, the measured $CP$ asymmetry $\mathcal{A}_{C\!P}(D^0\to\gamma \bar K^{*0})=(-0.7\pm5.0_{\rm stat.} \pm4.1_{\rm syst.})\%$ is consistent with $CP$ conservation.