Cabaye underwent the surgery earlier this week after being sidelined since the defeat at home to West Ham on November 11.
The French international was happy with the operation and is hopeful of being fit to return to action for Alan Pardew's side in early February.
"Surgery went off smoothly. It was done in two steps as the surgeon told me - on Monday right side and Tuesday left side," Cabaye told L'Equipe.
"Being back to competition early in February? That is the objective."