We report the first measurement of the flux-integrated cross section of $\nu_{\mu}$ charged-current single $\pi^{0}$ production on argon. This measurement is performed with the MicroBooNE detector, an 85 ton active mass liquid argon time projection chamber exposed to the Booster Neutrino Beam at Fermilab. This result on argon is compared to past measurements on lighter nuclei to investigate the scaling assumptions used in models of the production and transport of pions in neutrino-nucleus scattering. The techniques used are an important demonstration of the successful reconstruction and analysis of neutrino interactions producing electromagnetic final states using a liquid argon time projection chamber operating at the earth's surface.