The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theoretically addressed within the frameworks of classical electrodynamics and the time-dependent density functional theory (TDDFT). A fully quantum many-body description of the electron dynamics within TDDFT allows for analyzing the effect of electronic coupling between the emitter and the nanoantenna, usually ignored in classical descriptions of the optical response. We show that the hybridization between the electronic states of the quantum emitter and those of the metallic nanoparticles strongly modifies the energy, the width, and the very existence of the optical resonances of the coupled system. We thus conclude that the application of a quantum many-body treatment that correctly addresses charge-transfer processes between the emitter and the nanoantenna is crucial to address complex electronic processes involving plasmon–exciton interactions directly impacting optoelectronic applications.