Pauli blocking of interband transistions gives rise to tunable optical properties in single layer graphene (SLG). This effect is exploited in a graphene-nanoantenna hybrid device where Fano resonant plasmonic nanostructures are fabricated on top of a graphene sheet. The use of Fano resonant elements enhances the interaction of incident radiation with the graphene sheet and enables efficient electrical modulation of the plasmonic resonance. We observe electrically controlled damping in the Fano resonances occurring at approximately 2 μm, and the results are verified by full-wave 3D finite-element simulations. Our approach can be used for development of next generation of tunable plasmonic and hybrid nanophotonic devices.