We report results from a search for neutrino-induced neutral current (NC) resonant Δ(1232) baryon production followed by Δ radiative decay, with a ⟨0.8⟩  GeV neutrino beam. Data corresponding to MicroBooNE's first three years of operations (6.80×10^{20} protons on target) are used to select single-photon events with one or zero protons and without charged leptons in the final state (1γ1p and 1γ0p, respectively). The background is constrained via an in situ high-purity measurement of NC π^{0} events, made possible via dedicated 2γ1p and 2γ0p selections. A total of 16 and 153 events are observed for the 1γ1p and 1γ0p selections, respectively, compared to a constrained background prediction of 20.5±3.65(syst) and 145.1±13.8(syst) events. The data lead to a bound on an anomalous enhancement of the normalization of NC Δ radiative decay of less than 2.3 times the predicted nominal rate for this process at the 90% confidence level (C.L.). The measurement disfavors a candidate photon interpretation of the MiniBooNE low-energy excess as a factor of 3.18 times the nominal NC Δ radiative decay rate at the 94.8% C.L., in favor of the nominal prediction, and represents a greater than 50-fold improvement over the world's best limit on single-photon production in NC interactions in the sub-GeV neutrino energy range.