Using ab initio calculations we investigate the energy level alignment at the graphene/MoS2 heterostructure and the use of electron doping as a strategy to lower the Schottky barrier and achieve a low-resistance Ohmic contact. For the neutral heterostructure, density functional theory (DFT) with a generalized gradient approximation predicts a Schottky barrier height of 0.18 eV, whereas the G0W0 method increases this value to 0.60 eV. While the DFT band gap of MoS2 does not change when the heterostructure is formed, the G0W0 gap is reduced by 0.30 eV as a result of the enhanced screening by the graphene layer. In contrast to the case of metal substrates, where the band alignment is governed by Pauli repulsion-induced interface dipoles, the graphene/MoS2 heterostructure shows only a negligible interface dipole. As a consequence, the band alignment at the neutral heterostructure is not changed when the two layers are brought into contact. We systematically follow the band alignment as a function of doping concentration and find that the Fermi level of the graphene crosses the MoS2 conduction band at a doping concentration of around 1012 cm–2. The variation of the energy levels with doping concentration is shown to be mainly governed by the electrostatic potential resulting from the doping charge.