The 31-year-old Carter had been expected to play the first Rugby Championship match against Australia in Sydney last month but pulled up with the injury at training and missed the return fixture in Wellington.
Aaron Cruden and then debutant Tom Taylor played in the two wins instead with Beauden Barrett also out injured with a calf strain.
Barrett was named as the replacement fly-half on Thursday for the match at Waikato Stadium with Cruden (knee) and Taylor (ribs) not considered because of injury.
Injured NZ fly-half Carter sidelined for up to month
Carter's return to the side allowed coach Steve Hansen to give inside centre Saili his first test cap and allow Ma'a Nonu an opportunity to rest an ankle injury he sustained before the Rugby Championship.
Nonu played with the injury against Australia but with a potential title-decider next week in Auckland against South Africa, Hansen was taking no chances with the 31-year-old's recovery.
"With Ma'a's ongoing niggly ankle we have taken the opportunity to rest him and introduce Francis to international rugby," Hansen said upon naming his team. "We have complete faith in his ability to do the job.
"He is a very exciting, young player who has a multi-talented skillset that should suit test rugby."
Saili is a renowned line breaker at Super Rugby level with soft hands and good distribution skills, though he is prone to attempt too much rather than hold the ball and allow his side to build more pressure.
Any nerves the 22-year-old has on his debut will no doubt be lessened by the vast experience of Carter and Conrad Smith around him.
Hansen was forced into one other injury-enforced change with Owen Franks out with a groin injury, allowing Charlie Faumuina to test his scrummaging skills against the Pumas pack.
"With regard to the Argentinians, we are expecting a very physical encounter but also one that will see them use the flair and talent of their backline," Hansen added.
Argentina have yet to win a match in 16 previous internationals against the All Blacks, with their best result a 21-21 draw in 1985.
New Zealand: 15-Israel Dagg, 14-Ben Smith, 13-Conrad Smith, 12-Francis Saili, 11-Julian Savea, 10-Daniel Carter, 9-Aaron Smith, 8-Kieran Read, 7-Richie McCaw (captain), 6-Steven Luatua, 5-Sam Whitelock, 4-Brodie Retallick, 3-Charlie Faumuina, 2-Andrew Hore, 1-Tony Woodcock
Replacements: 16-Dane Coles, 17-Wyatt Crockett, 18-Ben Franks, 19-Jeremy Thrush, 20-Sam Cane, 21-Tawera Kerr-Barlow, 22-Beauden Barrett, 23-Charles Piutau
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