We present a measurement of $\eta$ production from neutrino interactions on argon with the MicroBooNE detector. The modeling of resonant neutrino interactions on argon is a critical aspect of the neutrino oscillation physics program being carried out by the DUNE and Short Baseline Neutrino programs. $\eta$ production in neutrino interactions provides a powerful new probe of resonant interactions, complementary to pion channels, and is particularly suited to the study of higher-order resonances beyond the $\Delta(1232)$. We measure a flux-integrated cross section for neutrino-induced $\eta$ production on argon of $3.22 \pm 0.84 \; \textrm{(stat.)} \pm 0.86 \; \textrm{(syst.)}$ $10^{-41}{\textrm{cm}}^{2}$/nucleon. By demonstrating the successful reconstruction of the two photons resulting from $\eta$ production, this analysis enables a novel calibration technique for electromagnetic showers in GeV accelerator neutrino experiments.