Retallick takes over from No.8 Ardie Savea, who suffered a head knock in last week's win over the Wallabies in Perth and was replaced after failing a head injury assessment (HIA).
Retallick, who has 86 test caps, is the fifth All Blacks captain this year.
In the forwards, hooker Asafo Aumua will be making his first test start, replacing Codie Taylor, who also failed an HIA in last weekend's Bledisloe Cup victory.
Prop Karl Tu'inukuafe comes in for George Bower while Joe Moody will make his return to international rugby via the bench after undergoing foot surgery this year.
Tyrel Lomax is the other reserve prop, coming into the 23 for his third test of the year.
Samisoni Taukei'aho is reserve hooker.
In the second row, Scott Barrett will once again start alongside Retallick, with Tupou Vaa'i again the reserve lock.
In the loose forwards, Luke Jacobson replaces Savea at No.8 for his third test start of the year, alongside Akira Ioane at blindside and Dalton Papalii at openside.
Ethan Blackadder provides loose forward cover in the reserves.
In the backs, TJ Perenara starts at halfback pushing Brad Weber to the bench.
Beauden Barrett is retained at first-five in his 95th Test.
David Havili and Anton Lienert-Brown are again the midfield pairing, while George Bridge will start on the left wing pushing Rieko Ioane to the bench.
Sevu Reece starts on the right wing with Jordie Barrett again at fullback.
Damian McKenzie is on the bench for a second straight week.
All Blacks coach Ian Foster said he was delighted to name Retallick as the captain for this Test.
"Brodie is a great leader in this team and we don't take his leadership for granted. We think this is a great honour for him, and he and his family can be hugely proud. He's playing really well and leads from the front. He has come back into the black jersey this year and just picked up where he left off.
"He also has an experienced partner in Beaudy (Barrett) alongside him who is bringing a calmness to the team and a sense of direction and we're seeing that in the way he plays."
Foster said that rotation would play a role in team selection with such a long campaign ahead, including the end of year tour.
"We've had a great build up in Perth and we're looking forward to getting to Queensland to finish our preparation. The key to selection this week has been about managing the player workload across the whole squad, which I think all teams will be doing in the Championship. We want to ensure we have a fresh, excited squad ready to play a physical and passionate Argentinian team.
"They've had a tough time on the road with matches in Europe and South Africa before coming to Australia. But we know from last year that when they spend a lot of time together it really unifies them, so we're expecting a torrid game."
The All Blacks and Argentina will be playing their 32nd Test against each other.
New Zealand has won 29 of those matches, with one draw and Argentina's first-ever victory in Sydney last year.
The last Test was a 38-0 win to the All Blacks in Newcastle last year.