Cross sections for the interaction ${\nu }_{\mu }A\to {\mu }^{-}{\pi }^{0}X$ 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 ${\pi }^0$, 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 ($3.57\pm 0.44)\times {10}^{-39}{\mathrm{cm}}^2$ is 7.5% higher than the genie prediction, but is consistent within experimental errors.