We report the first measurement of $\pi^0$ production in neutral current (NC) interactions on argon with average neutrino energy of $\lesssim1$~GeV. We use data from the MicroBooNE detector's 85-tonne active volume liquid argon time projection chamber situated in Fermilab's Booster Neutrino Beam and exposed to $5.89\times10^{20}$ protons on target for this measurement. Measurements of NC $\pi^0$ events are reported for two exclusive event topologies without charged pions. Those include a topology with two photons from the decay of the $\pi^0$ and one proton and a topology with two photons and zero protons. Flux-averaged cross-sections for each exclusive topology and for their semi-inclusive combination are extracted (efficiency-correcting for two-plus proton final states), and the results are compared to predictions from the \textsc{genie}, \textsc{neut}, and \textsc{NuWro} neutrino event generators. We measure cross sections of $1.243\pm0.185$ (syst) $\pm0.076$ (stat), $0.444\pm0.098\pm0.047$, and $0.624\pm0.131\pm0.075$ $[10^{-38}\textrm{cm}^2/\textrm{Ar}]$ for the semi-inclusive NC$\pi^0$, exclusive NC$\pi^0$+1p, and exclusive NC$\pi^0$+0p processes, respectively.