We report on the observation of terahertz (THz) radiation induced band-to-band impact ionization in HgTe quantum well (QW) structures of critical thickness, which are characterized by a nearly linear energy dispersion. The THz electric field drives the carriers initializing electron-hole pair generation. The carrier multiplication is observed for photon energies less than the energy gap under the condition that the product of the radiation angular frequency omega and momentum relaxation time tau(l) larger than unity. In this case, the charge carriers acquire high energies solely because of collisions in the presence of a high-frequency electric field. The developed microscopic theory shows that the probability of the light-induced impact ionization is proportional to exp(-E02/E2), with the radiation electric field amplitude E and the characteristic field parameter E-0. As observed in experiment, it exhibits a strong frequency dependence for omega tau >> 1 characterized by the characteristic field E-0 linearly increasing with the radiation frequency omega.