This article presents the first search for neutrino-induced neutral current coherent single-photon production (NC coherent 1$\gamma$). The search makes use of data from the MicroBooNE 85-tonne active volume liquid argon time projection chamber detector, situated in the Fermilab Booster Neutrino Beam (BNB), with an average neutrino energy of $⟨E_{\nu }⟩\sim 0.8$~GeV. A targeted selection of candidate neutrino interactions with a single photon-like electromagnetic shower in the final state and no visible vertex activity was developed to search for the NC coherent 1$\gamma$ process, along with two auxiliary selections used to constrain the dominant background from NC${\pi }^0$ production. With an integrated exposure of $6.87\times {10}^{20}$ protons on target delivered by the BNB, we set the world’s first limit for this rare process, corresponding to an upper limit on the flux-averaged cross section of $\sigma <1.49\times {10}^{-41}{\mathrm{\text{cm}}}^2$ at 90% C.L.