We present a time-resolved optical study of recently developed narrow-line MoSe 2 monolayers grown on hexagonal boron nitride with means of molecular beam epitaxy. We find that the photoluminescence decay times are significantly shorter than in the case of the exfoliated samples, even below one picosecond. Such a short timescale requires measurements with better resolution than achievable with a streak camera. Therefore, we employ an excitation correlation spectroscopy pump-probe technique. This approach allows us to identify two distinct non-radiative recombination channels attributed to lattice imperfections. The first channel is active at helium temperatures. It reduces the lifetime of the neutral exciton to below one picosecond. The second channel becomes active at elevated temperatures, further shortening the lifetimes of both neutral and charged exciton. The high effectiveness of both radiative and non-radiative recombination makes epitaxial MoSe 2 a promising material for ultrafast optoelectronics.