Nova Monocerotis 2012 is the third γ-ray transient identified with a thermonuclear runaway on a white dwarf, that is, a nova event. Swift monitoring has revealed the distinct evolution of the harder and super-soft X-ray spectral components, while Swift-UV and V- and I-band photometry show a gradual decline with subtle changes of slope. During the super-soft emission phase, a coherent 7.1 hr modulation was found in the soft X-ray, UV, optical, and near-IR data, varying in phase across all wavebands. Assuming this period to be orbital, the system has a near-main-sequence secondary, with little appreciable stellar wind. This distinguishes it from the first GeV nova, V407 Cyg, where the γ-rays were proposed to form through shock-accelerated particles as the ejecta interacted with the red giant wind. We favor a model in which the γ-rays arise from the shock of the ejecta with material close to the white dwarf in the orbital plane. This suggests that classical novae may commonly be GeV sources. We ascribe the orbital modulation to a raised section of an accretion disk passing through the line of sight, periodically blocking and reflecting much of the emission. The disk must therefore have reformed by day 150 after outburst