Nonlocal electromagnetic effects of graphene arise from its naturally dispersive dielectric response. We present semianalytical solutions of nonlocal Maxwell's equations for graphene nanoribbon arrays with features around 100 nm, where we found prominent departures from its local response. Interestingly, the nonlocal corrections are stronger for light polarization parallel to the ribbons, which manifests as an additional broadening of the Drude peak. For the perpendicular polarization case, nonlocal effects lead to blue-shifts of the plasmon peaks. These manifestations provide a physical measure of nonlocal effects, and we quantify their dependence on the ribbon width, doping, and wavelength.