Whitelock was hurt during the Super Rugby match on Friday between his Crusaders side and the Hamilton-based Chiefs. He is expected to be sidelined for up to six weeks.
The loss of Whitelock comes at a bad time for the All Blacks, following only days after veteran lock Ali Williams announced his retirement from international rugby.
GALLERY - Super Rugby - Round 15
Luke Romano and Brodie Retallick are now expected to lock the All Blacks' scrum against France, while 22-year-old Dominic Bird might get his first taste of Test rugby from the bench.