We demonstrate that, as in the forward cascade of three-dimensional turbulence that displays intermittency (a lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display a lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two-dimensional turbulence are examined, using different forcing functions of the same forcing length scale but different fractal dimension D that varies from the classical D=2 case to the point vortex case D=0. It is shown that as the fractal dimension of the forcing is decreased from D=2, the self-similarity is lost and intermittency appears. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multifractal models of turbulence.