The 29-year-old damaged his right knee at the back end of last year.
He has already been sidelined for a month but faces between a further five to eight weeks out, according to Clermont medical staff.
Smit has only played two Top 14 games for Les Auvergnats since joining them in November.
Coach Vern Cotter has Argentina international Mario Ledesma as cover during the Springbok's absence.
