Transition metal dichalcogenide monolayers are promising candidates for exploring new electronic and optical phenomena and for realizing atomically thin optoelectronic devices. They host tightly bound electron-hole pairs (excitons) that can be efficiently excited by resonant light fields. Here, we demonstrate that a single monolayer of molybdenum diselenide (MoSe2) can dramatically modify light transmission near the excitonic resonance, acting as an electrically switchable mirror that reflects up to 85% of incident light at cryogenic temperatures. This high reflectance is a direct consequence of the excellent coherence properties of excitons in this atomically thin semiconductor, encapsulated by hexagonal boron nitride. Furthermore, we show that the MoSe2 monolayer exhibits power- and wavelength-dependent nonlinearities that stem from exciton-based lattice heating in the case of continuous-wave excitation and exciton-exciton interactions when fast, pulsed laser excitation is used. These observations open up new possibilities for studying quantum nonlinear optical phenomena and topological photonics, and for miniaturizing optical devices.