The 29-year-old was originally named in the All Blacks' starting 15 but has now had to withdraw.
It is now feared that the number 10 may miss out on the rest of the tournament and the All Blacks are set to release a statement regarding the extent of the injury on Sunday.
"Carter will be further assessed this evening [Saturday] and an update will be given tomorrow," said an All Blacks statement. "No further updates will be given at this time."
Carter is currently the all-time highest points scorer in Test match rugby with 1250 points.