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McCaw withdrew earlier on Saturday citing an ongoing foot problem and Carter took over the captaincy for Sunday's Pool A Clash with the Canadians.
Carter, however, limped out of training later in the day with a groin injury while practicing kicking and would be assessed by medical staff, the team said in a statement.
Colin Slade replaces Carter at flyhalf with hooker Andrew Hore named the new captain.
McCaw, who will be replaced by Victor Vito for the match, said he decided to withdraw because of a "niggly" foot injury that forced him to miss part of this year's Super rugby season. He had surgery in an attempt to fix the issue.
"My foot is a bit niggly. It's something I have managed all the way through," McCaw told reporters in Wellington. "If I had to play tomorrow in a knockout game I would have, but the decision was to make sure I'm right next week."
The All Blacks have already secured top spot in Pool A and a quarter-final berth with wins over Tonga, Japan and France. They will play the runners-up in Pool B, likely to be Argentina, in the quarter-finals next week.
"I probably could have played (against Canada) but it's the cumulative effect where it might take an extra day (to recover) because of the extra load I have had," McCaw said.
"You play at times with niggles every week, it's just the reality of every player, you play with those things.
"(But) there is a difference between (being) tough and playing because you're a bit sore and being stupid.
"At times you just play when you can do your job properly without doing anything silly. But there comes a point where you don't play because obviously you can't do your job."
The match will be the second McCaw has missed at the World Cup after he was a late withdrawal from the side to play Japan but he was confident he should be available for every game through the knockout phases.
Carter also missed the Japan game with a back injury.
"You haven't got a crystal ball but if it has been like it has all week then it should be okay (to play three successive knockout games if needed).
"It's something I have dealt with up till this point and it's something I have to deal with.
"I've had my head around it for a long time and if you're going to play it's something you have to manage."