The emergent class of atomically thin two-dimensional (2D) materials has opened up completely new opportunities for manipulating electronic quantum states at the nanoscale. Here we explore the concept of dielectric band gap engineering, i.e., the controlled manipulation of the band gap of a semiconductor via its dielectric environment. Using first-principles calculations based on the GW self-energy approximation we show that the band gap of a two-dimensional (2D) semiconductor, such as the transition metal dichalcogenides, can be tuned over several hundreds of meV by varying the doping concentration in a nearby graphene sheet. Importantly, these significant band gap renormalizations are achieved via nonlocal Coulomb interactions and do not affect the structural or electronic integrity of the 2D semiconductor. We investigate various heterostructure designs, and show that, depending on the size of the intrinsic dielectric function of the 2D semiconductor, the band gap can be tuned by up to 1 eV for graphene carrier concentrations reachable by electrostatic doping. Our work provides opportunities for electrically controllable band gap engineering in 2D semiconductors.