The first observation of the Bs0→D̄∗0φ decay is reported, with a significance of more than seven standard deviations, from an analysis of pp collision data corresponding to an integrated luminosity of 3 fb-1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction is measured relative to that of the topologically similar decay B0→D̄0π+π- and is found to be B(Bs0→D̄∗0φ)=(3.7±0.5±0.3±0.2)×10-5, where the first uncertainty is statistical, the second systematic, and the third from the branching fraction of the B0→D̄0π+π- decay. The fraction of longitudinal polarization in this decay is measured to be fL=(73±15±4)%. The most precise determination of the branching fraction for the Bs0→D̄0φ decay is also obtained, B(Bs0→D̄0φ)=(3.0±0.3±0.2±0.2)×10-5. An upper limit, B(B0→D̄0φ)<2.0 (2.3)×10-6 at 90% (95%) confidence level is set. A constraint on the ω-φ mixing angle δ is set at |δ|<5.2° (5.5°) at 90% (95%) confidence level.