In the present work, we report different interlayer excitonic states of an aligned MoSe2/MoS2 incommensurate van der Waals (vdW) heterostructure (HS). The HS was fabricated by stacking chemical vapor deposited monolayers, and it was studied using photoluminescence (PL) measurements. We observed the emergence of two low-energy peaks in the PL spectrum of the HS measured at 100 K, which were absent in the constituent monolayers. The orbital resolved electronic band structure and the optical absorption considering the electron-hole interaction for these HSs were calculated using first-principles density functional theory simulations, which showed energy band hybridization and the presence of interlayer excitons (ILEs). Based on these observations, the peak at ∼1.57 eV was assigned to a momentum direct ILE, while the other peak at ∼1.35 eV showed feeble emission intensity and was assigned to a momentum indirect ILE. The emergence of both of these excitonic peaks in the HS PL spectrum can be attributed to the formation of a spatially periodic moiré potential at a nanometer length scale resulting in hybridization. Our results can help to understand the physics of ILEs and to engineer vdW HSs for efficient optoelectronic devices. © 2021 American Physical Society.