The 30-year-old Carter, capped 93 times for New Zealand and Test rugby's highest points scorer, pulled up in training on Thursday with "a leg twinge".
The playmaker's replacement will be understudy Aaron Cruden, with Beauden Barrett moving on to the bench.
"Gutted not to be playing with these boys in this stadium tomorrow," Carter tweeted along with a photo of the Millennium Stadium.
All Blacks captain Richie McCaw said injuries in rugby were something to be expected, saying that the important thing now was to focus on handing Cruden as comfortable a ride as possible.
"It's something you can't control. Aaron's played a few Tests, some pretty big games," said McCaw.
"It's disappointing for Dan, but the next guy will come in and we'll try to give him some good ball to operate with.
"Dan's a pretty good footballer, 90-something Tests, he's hard to replace. But we've got to get on, and have belief in the next guys."
Indeed, the All Blacks managed to replace Carter in the World Cup, the playmaker ruled out for the semi-finals and final that New Zealand won, with Cruden, Colin Slade and finally Stephen MacDonald.
Turning to Saturday's match, McCaw said: "The boys are in pretty good shape and we all want to play now.
"We're expecting a Welsh team to come out and front up. We certainly respect the way they go about things," he said in reference to the home side's five-match losing streak, including defeats by Argentina and Samoa in the two previous weekends.
Worringly for Wales, McCaw insisted that his side had not yet peaked, despite adding the inaugural Rugby Championship crown to their World Cup title.
And history will definitely not be on Wales' side. The match is the 29th Test match between the two teams, with the All Blacks having won 25 times, and Wales' last victory coming way back in 1953.
"We want to put together a much better performance over the 80 minutes," said openside flanker McCaw.
"The big motivation is backing up good performances.
"This group of players want to perform and take a step up from the last couple of weeks.
"We've done a lot of good things this year but we haven't reached our full potential yet."
McCaw added: "Tomorrow's a big challenge. Wales have played a lot of Tests. Give them a bit of space and time and they're good players.
"We're going to play the game we need to."