In this paper, we propose a novel quantum approach for microwave-to-optical conversion in a multilayer graphene structure. The graphene layers are electrically connected and pumped by an optical field. The physical concept is based on using a driving microwave signal to modulate the optical input pump by controlling graphene conductivity. Consequently, upper and lower optical sidebands are generated. To achieve low noise conversion, the lower sideband is suppressed by the multilayer graphene destruction resonance. A perturbation approach is implemented to model the effective permittivity of the electrically driven multilayer graphene. Subsequently, a quantum mechanical analysis is carried out to describe the evolution of the interacting fields. It is shown that a quantum microwave-to-optical conversion is achieved for miltilayer graphene of the proper length (i.e., number of layers). The conversion rate and the number of converted photons are evaluated according to several parameters. These include the microwave signal frequency, the microwave driving voltages, the graphene intrinsic electron density, and the number of graphene layers. Owing to multilayer dispersion and to the properties of graphene, it is shown that a significant number of photons (converted from microwave to optical frequency range) is achieved for microvolt microwave driving voltages. Furthermore, a frequency-tunable operation is achieved using this technique simply by modifying the optical pump frequency.