We report light emission around 1 eV (1240 nm) from heterostructures of MoS_{2} and WSe_{2} transition metal dichalcogenide monolayers. We identify its origin in an interlayer exciton (ILX) by its wide spectral tunability under an out-of-plane electric field. From the static dipole moment of the state, its temperature and twist-angle dependence, and comparison with electronic structure calculations, we assign this ILX to the fundamental interlayer transition between the K valleys in this system. Our findings gain access to the interlayer physics of the intrinsically incommensurate MoS_{2}/WSe_{2} heterostructure, including moiré and valley pseudospin effects, and its integration with silicon photonics and optical fiber communication systems operating at wavelengths longer than 1150 nm.