Based on $e^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of 7.93~$f{b}^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider, the absolute branching fractions of the decays $D^0\to K_S^0\omega$ and $D^0\to K_L^0\omega$ are measured to be $(11.73\pm 0.18\pm 0.25\pm 0.47)\times {10}^{-3}$ and $(11.01 )×10^{−3}, respectively. The $K_S^0-K_L^0$ branching-fraction asymmetry of these two decays is $R(D^0,K_{S,L}^0\omega )=\frac{ℬ(D^0\to K_S^0\omega )-ℬ(D^0\to K_L^0\omega )}{ℬ(D^0\to K_S^0\omega )+ℬ(D^0\to K_L^0\omega )}=(3.2\pm 1.0\pm 0.9\pm 2.8)\%$. Here, the first uncertainties are statistical, the second systematic, and the third arise from the interference between $D^0\to K_{S,L}^0\omega$ and the non-resonant $D^{0} ^{+}{-}^{0} K_{S,L}^{0} $ processes.