Cross sections for the interaction ν A → μ −π X with neutrino energies between 1 and 5 GeV are measured using a sample of 165,000 selected events collected in the NOvA experiment's near detector, a hydrocarbon-based detector exposed to the Neutrinos from the Main Injector beam at the Fermi National Accelerator Laboratory. Results are presented as a flux-averaged total cross section and as differential cross sections in the momenta and angles of the outgoing muon and π, the total four-momentum transfer, and the invariant mass of the hadronic system. Comparisons are made with predictions from a reference version of the genie neutrino interaction generator. The measured total cross section of (3.57 ± 0.44) 10 cm is 7.5% higher than the genie prediction, but is consistent within experimental errors.