Thuram has not played since the end of last season due to degeneration of the cartilage in his kneecap.
Reports from Gazzetta dello Sport and Sky Italia said the 25-year-old, the younger brother of Inter winger Marcus and son of former France defender Lilian, would be out for at least four months.
Khephren Thuram has scored six goals in 70 Serie A appearances for Juve in two seasons since signing from Ligue 1 side Nice.
Juventus missed out on Champions League qualification by finishing sixth in Italy's top flight last term, but have won their first two Serie A matches of the new campaign.