We analyze theoretically the dynamical transport through a weakly coupled semiconductor superlattice, under an ac potential with frequencies in the THz regime, by means of a general model for time-dependent sequential tunneling within a nonequilibrium-Green's-function framework. Highly doped superlattices present, under certain conditions, the formation of electric-field domains at a static dc voltage bias. We find that the THz signal drives the system from a stationary current toward an oscillatory time dependence as the ac intensity increases. However, the current oscillates periodically in the MHz regime, reflecting an ac-induced motion and recycling of traveling domain walls. Finally, we predict that on further increasing the intensity of the ac potential, the tunneling current undergoes a transition from a periodically time-dependent state to a stationary one in which a homogeneous electric-field distribution builds up along the sample.