Fly-half Carter had been named captain following the withdrawal of Richie McCaw earlier on Saturday with a foot injury.
But now the All Blacks have confirmed Carter has pulled out with a groin injury sustained in training.
Colin Slade is now set to start, with hooker Andrew Hore named captain.
Carter suffered the injury during kicking practice at the captain's run training session at Rugby League Park in Wellington on Saturday afternoon and will undergo tests to determine the full extent of his injury.
A New Zealand team statement read: "Carter will be further assessed this evening and an update will be given tomorrow.
"No further updates will be given at this time."
Carter had been due to captain New Zealand for the first time in the absence of flanker McCaw, who had been set to win his 101st cap tomorrow.
But McCaw was replaced by Victor Vito in the back row due to a foot problem.
McCaw is confident he will be fit for the quarter-finals.
He said: "It's something I have managed all the way through (the season) and it gets a bit niggly at times and I manage it through the early start of a week.
"After Saturday's game (against France) it was no different and I managed it through the early part of the week, got through training fine yesterday, but it was just a bit niggly this morning.
"I was pretty keen to play against Canada because it's important for the team and for all of us that we carry on the momentum, but obviously we have a knockout game next week and I just wanted to make sure it wasn't niggly heading into that week.
"So that's the reason for the decision."
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