We report a measurement of the branching fraction for τ − → π − π 0 ν τ and the invariant mass spectrum of the resulting π − π 0 system using 72.2 fb −1 of data recorded by the Belle detector at the KEKB e + e − collider. The branching fraction obtained is (25.15 ± 0.04 ± 0.31)%, where the first error is statistical and the second is systematic. The unfolded π − π 0 mass spectrum is used to determine resonance parameters for the ρ(770), ρ ′ (1450), and ρ ′′ (1700) mesons. We also use this spectrum to estimate the hadronic contribution to the anomalous magnetic moment of the muon.