The behavior of excitons in van der Waals (vdWs) heterostructures depends on electron-electron interactions and charge transfer at the hetero-interface. However, what still remains to be unraveled is to which extent the carrier densities of both counterparts and the band alignment in the vdWs heterostructures determine the photoluminescence properties. Here, we systematically study the photoluminescence properties of monolayer MoS2/graphene heterostructures by modulating the carrier densities and contact barrier at the interface via electrochemical gating. It is shown that the PL intensities of excitons can be tuned by more than two orders of magnitude, and a blue-shift of the exciton peak of up to 40 meV is observed. By extracting the carrier density of MoS2 using an electric potential distribution model, and the Schottky barrier using first-principle calculations, we find that the controllable carrier density in MoS2 plays a dominant role in the PL tuning at negative gate bias, whereas the interlayer relaxation of excitons induced by the Schottky barrier has a major contribution at positive gate bias. This is further verified by controlling the tunneling barrier and screening field across MoS2 by inserting self-assembled monolayers (SAMs) at the interface. These findings will benefit to better understand the effect of many-body interactions and hetero-interfaces on the optical and optoelectronic properties in vdWs heterostructures.