In this paper, we report on the study of the optical properties of YAG:Ce and GGG:Ce garnet crystals after irradiation in a 660~MeV proton beam with a fluence up to 8.9$times$10$^{14}$ protons/cm$^2$. We found that the transparency of both crystals fell by no more than 7% in the region of their own luminescence. The light yield of a YAG:Ce sample, measured one year after irradiation, dropped by about 35%.