The influence of optical illumination on transmission of THz radiation through a bulk crystal of semi-insulating GaAs is experimentally studied. It is established that, without additional illumination, absorption of electromagnetic waves with a frequency of about 1 THz in the studied crystal is almost absent. Optical illumination in the spectral range of fundamental absorption of the crystal does not affect the transmission of THz waves. At the same time, if the illumination photon energy is a little below the edge of fundamental absorption, i.e., actually in the transparency region, the transmission of THz radiation drops sharply. At liquid helium temperature, the maximum effect is achieved for the energy of optical photons lower by approximately 30 meV than the crystal band gap. Further shift of the illumination toward lower photon energies is accompanied by almost complete recovery of the transmission. With increasing sample temperature, the spectral range of efficient action of the illumination shifts together with the edge of fundamental absorption toward lower photon energies.