Using 4.7 fb^{-1} of e^{+}e^{-} collision data at center-of-mass energies from 4.661 to 4.951 GeV collected by the BESIII detector at the BEPCII collider, we observe the X(3872) production process e^{+}e^{-}→ωX(3872) for the first time. The significance is 7.8σ, including both the statistical and systematic uncertainties. The e^{+}e^{-}→ωX(3872) Born cross section and the corresponding upper limit at 90% confidence level at each energy point are reported. The line shape of the cross section indicates that the ωX(3872) signals may be from the decays of some nontrivial structures.