Blues first five Harry Plummer has also been added to the squad after an injury to Stephen Perofeta.
Barrett injured a finger during the All Blacks 47-5 win against Fiji in San Diego, which required a surgical treatment after his return to New Zealand.
Assistant coach Jason Ryan made the changes public on Monday at the team's base at the NZCIS campus in Upper Hutt.
Ryan said that the All Blacks have "definitely got to build up from where we left off pretty quickly" after three wins to start the season.
"Argentina bring a different intensity to the first three tests that we had…it should be a good contest, they've been playing really well," Ryan said of Pumas, who split a series 1-1 with France and demolished neighbours Uruguay in their three tests so far in 2024.
"I think they've always been a passionate side, they play with energy and momentum. (Matias) Kremer and (Pablo) Matera are big around the breakdown."
yan said that the focus now the squad had reassembled for the Rugby Championship was to adapt to challenge that the Pumas, Springboks and Wallabies would pose.
"You've always got to be evolving your game, week to week. We're always trying to tweak things."
As for what the biggest work on was after the two English victories, Ryan pointed to the breakdown.
"We learned a lot around our carry and clean game. We were really accurate around our decision-making, we're looking forward to building off our scrum and set piece.
"We've got some good lads who made contributions in our loosies, our locks are a competitive area…yeah I think we've got a lot of confidence in everyone. It makes selection meetings a bit tastier."
All Blacks v Pumas
Kick-off: 7.05pm, Saturday, August 10 (NZT)
Sky Stadium, Wellington
Teams will be announced on Thursday.
