We present the results of a study of the charmless vector-vector decay B0→ωK*0 with 657×106 BB̅ pairs collected with the Belle detector at the KEKB e+e- collider. We measure the branching fraction to be B(B0→ωK*0)=[1.8±0.7(stat)±0.3(syst)]×10-6 with 3.0σ significance. We also perform a helicity analysis of the ω and K*0 vector mesons, and obtain the longitudinal polarization fraction fL(B0→ωK*0)=0.56±0.29(stat)-0.08+0.18(syst). Finally, we measure a large nonresonant branching fraction B[B0→ωK+π-;MKπ∈(0.755,1.250)  GeV/c2 ]=[5.1±0.7(stat)±0.7(syst)]×10-6 with a significance of 9.5σ.