An analysis is done of the ionization of deep impurity centers by high-intensity terahertz radiation, with photon energies tens of times lower than the impurity ionization energy. Under these conditions, ionization can be described as direct tunneling and 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. 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 of tunneling as compared to static fields was observed. The transition between the quasi-static and the high frequency regime is determined by the tunneling time. For the case of deep impurities this is the time of redistribution of the defect vibrational system which depends strongly on temperature and the impurity structure.