An analysis is made of the ionization of deep impurity centers induced by high-intensity terahertz radiation whose photon energies are tens of times lower than the impurity ionization energy. Under these conditions, ionization can be described as phonon-assisted tunneling in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field of the radiation. At high intensities the ionization is caused by direct tunneling. Within a broad range of intensity, frequency and temperature, the terahertz electric field of the radiation acts like a static field. For very high frequencies and low temperatures an enhancement in tunneling as compared to static fields takes place.