Carter was named in the team earlier on Thursday and appeared at a media conference but was then ruled out after a team training session.
"At training this morning it was apparent he would not be able to play," coach Steve Hansen said. "So we have done the sensible thing and withdrawn him from the Test match."
Hansen said Carter had been carrying the injury all week but it had been hoped he would recover in time for the Test at Wellington Regional Stadium.
Aaron Cruden will now start the match in place of Carter, while Beauden Barrett, who was not in the original 28-man squad but had been training with the team during Test weeks, will slot in on the bench.
Hansen has also recalled Conrad Smith for the match after the centre missed the two Bledisloe Cup Tests against Australia last month due to eye surgery.
Smith and Ma'a Nonu have had a long partnership at Super Rugby and international level and were the first choice centre pairing for the All Blacks during last year's World Cup campaign, though they have not played together since beating France to win the Webb Ellis trophy.
Smith had two surgeries on a detached retina following the conclusion of the Super Rugby tournament and was unavailable for the All Blacks victories over the Wallabies last month.
The 30-year-old Nonu was rested for the June internationals against Ireland, and when he returned to the side for the Rugby Championship he was moved out to centre to accommodate Sonny Bill Williams.
Williams has since left on a short-term playing contract in Japan and is then expected to link up with a rugby league club in Australia.
"He is probably the leading centre in the world at the moment," Hansen said of Smith. "His leadership, you can't put a value on it and having him back is great.
"The combination of Conrad and Ma'a has been around for a while and been very successful and we are expecting that combination to deliver."
Smith's return will bring greater balance to the backline, with Nonu and Williams both line-breaking players who appeared to lack a little cohesion in linking with their back three in the Tests against Australia.
"He is pretty good at getting with the line breaker and that should help," Hansen added.
"But converting line breaks is about us making the right decisions by both the ball carrier and the support carrier."
Hansen made three changes to the forwards from that which started at Eden Park against the Wallabies with Victor Vito replacing Liam Messam at blindside flanker while lock Brodie Retallick replaces Sam Whitelock.
Tony Woodcock has returned at loosehead prop after recovering from a rib injury sustained in the first match against Australia.
Both Messam and Whitelock move to the replacements bench from which versatile Auckland prop Charlie Faumuina could make his Test debut, with Hansen expecting a tough battle up front against the Pumas.
Meanwhile, Argentina coach Santiago Phelan finalised his team when he named his replacements bench.
The Pumas had named their starting side on Tuesday with fly-half Juan Martin Hernandez and openside flanker Juan Manuel Leguizamon returning to the side after injuries.
Both players missed Argentina's 16-16 draw with South Africa in Mendoza two weeks ago and will bring an added dimension to a Pumas side packed with experience and burning to stamp their credentials on the competition.
"We are really excited to play the match against New Zealand," centre Santiago Fernandez said. "They are the best in the world and we hope things go well.
"We have to try to put them under a lot of pressure, because if you let them play, they are lethal. They are the best in the world and if you have not closed spaces (they will punish you).
"We want to get a result, but we know we have to play a perfect game. We are positive."
New Zealand: 15-Israel Dagg, 14-Cory Jane, 13-Conrad Smith, 12-Ma'a Nonu, 11-Julian Savea, 10-Aaron Cruden, 9-Aaron Smith, 8-Kieran Read, 7-Richie McCaw (captain), 6-Victor Vito, 5-Brodie Retallick, 4-Luke Romano, 3-Owen Franks, 2-Keven Mealamu, 1-Tony Woodcock
Replacements: 16-Andrew Hore, 17-Charlie Faumuina, 18-Sam Whitelock, 19-Liam Messam, 20-Piri Weepu, 21-Beauden Barrett, 22-Ben Smith
Argentina: 15-Martin Rodriguez, 14-Gonzalo Camacho, 13-Marcelo Bosch, 12-Santiago Fernandez, 11-Horacio Agulla, 10-Juan Martin Hernandez, 9-Nicolas Vergallo, 8-Juan Martin Fernandez Lobbe (captain), 7-Juan Manuel Leguizamon, 6-Julio Farias Cabello, 5-Patricio Albacete, 4-Manuel Carizza, 3-Juan Figallo, 2-Eusebio Guinazu, 1-Rodrigo Roncero.
Replacements: 16-Agustin Creevy, 17-Marcos Ayerza, 18-Juan Pablo Orlandi, 19-Leonardo Senatore, 20-Thomas Leonardi, 21-Martin Landajo, 22-Lucas Gonzalez Amorosino