We report on a study of the decay B^0→D^(*+)ωπ^- with the BABAR detector at the PEP-II B-factory at the Stanford Linear Accelerator Center. Based on a sample of 232×10^6 BB decays, we measure the branching fraction B(B^0→D^(*+)ωπ^-)=(2.88±0.21(stat.)±0.31(syst.))×10^(-3). We study the invariant mass spectrum of the ωπ^- system in this decay. This spectrum is in good agreement with expectations based on factorization and the measured spectrum in τ-→ωπ-ν_τ. We also measure the polarization of the D^(*+) as a function of the ωπ^- mass. In the mass region 1.1 to 1.9 GeV we measure the fraction of longitudinal polarization of the D^(*+) to be ΓL/Γ=0.654±0.042(stat.)±0.016(syst.). This is in agreement with the expectations from heavy-quark effective theory and factorization assuming that the decay proceeds as B^(-0)→D^(*+)ρ(1450)-, ρ(1450)^-→ωπ^-
