In his absence, the club have signed Julien Caminati as a replacement.
Gross, 26, will undergo the operation on Friday and is expected to be out of action for several months, Castres said.
Caminati, 30, who can play on the wing or at full back, was signed by Toulon at the start of the season as cover for players missing on World Cup duty. He has previously played for Grenoble and Brive.