MeV-scale energy depositions by low-energy photons produced in neutrino-argon interactions have been identified and reconstructed in ArgoNeuT liquid argon time projection chamber (LArTPC) data. ArgoNeuT data collected on the NuMI beam at Fermilab were analyzed to select isolated low-energy depositions in the TPC volume. The total number, reconstructed energies and positions of these depositions have been compared to those from simulations of neutrino-argon interactions using the FLUKA Monte Carlo generator. Measured features are consistent with energy depositions from photons produced by de-excitation of the neutrino's target nucleus and by inelastic scattering of primary neutrons produced by neutrino-argon interactions. This study represents a successful reconstruction of physics at the MeV-scale in a LArTPC, a capability of crucial importance for detection and reconstruction of supernova and solar neutrino interactions in future large LArTPCs.