Among the many extraordinary properties of graphene, its optical response allows one to easily tune its interaction with nearby molecules via electrostatic doping. The large confinement displayed by plasmons in graphene nanodisks makes it possible to reach the strong-coupling regime with a nearby quantum emitter, such as a quantum dot or a molecule. In this limit, the quantum emitter can introduce a significant plasmon-plasmon interaction, which gives rise to a plasmon blockade effect. This produces, in turn, strongly nonlinear absorption cross sections and modified statistics of the bosonic plasmon mode. We characterize these phenomena by studying the equal-time second-order correlation function g((2))(0), which plunges below a value of 1, thus revealing the existence of nonclassical plasmon states. The plasmon-emitter coupling, and therefore the plasmon blockade, can be efficiently controlled by tuning the doping level of the graphene nanodisks. The proposed system emerges as a new promising platform to realize quantum plasmonic devices capable of commuting optical signals at the single-photon/plasmon level.