Graphene is known to possess strong optical nonlinearity which turned out to be suitable for creation of efficient saturable absorbers in mode locked fiber lasers. Nonlinear response of graphene can be further enhanced by the presence of graphene plasmons. Here, we report a novel nonlinear effect observed in nanostructured graphene which comes about due to excitation of graphene plasmons. We experimentally detect and theoretically explain enhanced mixing of near-infrared and mid-infrared light in arrays of graphene nanoribbons. Strong compression of light by graphene plasmons implies that the described effect of light mixing is nonlocal in nature and orders of magnitude larger than the conventional local graphene nonlinearity. Both second and third order nonlinear effects were observed in our experiments with the recalculated third-order nonlinearity coefficient reaching values of 4.5 × 10–6 esu. The suggested effect could be used in variety of applications including nonlinear light modulators, light multiplexers, light logic, and sensing devices.