We show that self-induced oscillations at frequencies above GHz and with a high spectral purity can be obtained in a silicon photonic crystal nanocavity under optical pumping. This self-pulsing results from the interplay between the nonlinear response of the cavity and the photon cavity lifetime. We provide a model to analyze the mechanisms governing the onset of self-pulsing, the amplitudes of both fundamental and harmonic oscillations and their dependences versus input power and oscillation frequency. Theoretically, oscillations at frequencies higher than 50 GHz could be achieved in this system.