Interfacing TMD monolayers with graphene enables the demonstration of bright, single and narrow-line photoluminescence arising solely from TMD neutral excitons. Atomically thin semiconductors made from transition metal dichalcogenides (TMDs) are model systems for investigations of strong light-matter interactions and applications in nanophotonics, optoelectronics and valleytronics. However, the photoluminescence spectra of TMD monolayers display a large number of features that are particularly challenging to decipher. On a practical level, monochromatic TMD-based emitters would be beneficial for low-dimensional devices, but this challenge is yet to be resolved. Here, we show that graphene, directly stacked onto TMD monolayers, enables single and narrow-line photoluminescence arising solely from TMD neutral excitons. This filtering effect stems from complete neutralization of the TMD by graphene, combined with selective non-radiative transfer of long-lived excitonic species to graphene. Our approach is applied to four tungsten- and molybdenum-based TMDs and establishes TMD/graphene heterostructures as a unique set of optoelectronic building blocks that are suitable for electroluminescent systems emitting visible and near-infrared photons at near THz rate with linewidths approaching the homogeneous limit.