Slade was selected to continue at fly-half following Carter's tournament-ending groin injury, in a New Zealand side showing six changes and one positional switch from the 79-15 defeat of Canada last weekend.
Much has been made of the loss of Carter - the world's leading playmaker - as the host nation wonders if their 24-year wait for World Cup glory will end on home soil on October 23.
But Henry is confident Slade can step up to the mark, starting when he wins his 10th cap against the Pumas in the last eight.
Henry said: "I've been pleased with him - I think he's getting better.
"He's getting more comfortable in the group. He's obviously the navigator of the team playing at 10, he's got to run the ship.
"And that's a big ask when he's playing with guys who have played 100 Test matches and 75 Test matches and so on and he's played 10 at most.
"It's a big ask for him, but he's getting more comfortable, he's enjoying the environment - I think he'll play well."
Mils Muliaina has also been retained in the starting XV and is set to win his 100th cap.
Ma'a Nonu and Corey Jane return to a back division which sees Sonny Bill Williams move to the wing and Piri Weepu take over at scrum-half.
In the forwards, captain Richie McCaw returns at flanker despite an ongoing foot injury, as do Keven Mealamu at hooker and Brad Thorn at lock.
McCaw's training has been curtailed by the problem, which will have to be nursed so long as New Zealand are in the tournament.
Henry added: "It's niggly and he's looking after it as best he can.
"It's just an ongoing thing. He's just got to do what he can during the week to perform at the weekend. He's controlling himself very well.
"He runs on it, feels good, wakes up the next day and feels niggly again.
"Hopefully we've got three games ahead of us and it's just a matter of trying to make sure he's available for those three games.
"He's got to tailor what he does running-wise to be able to handle that eventuality."
Muliaina retained his place and Williams was selected on the wing in part due to injuries to Zac Guildford (hamstring), Israel Dagg (thigh haematoma) and Richard Kahui (hamstring).
Henry added: "We just don't think (Dagg) is ready. Richard Kahui's got a hamstring and he's not that far away but he's a big risk, so we decided not to play those two."
With the All Blacks' leading back row available - McCaw joined by Kieran Read and Jerome Kaino - Victor Vito has been named on the bench ahead of Adam Thomson.
Henry said: "Thommo's not fit. That's the reason. He was selected initially in this team but hasn't come through training.
"He's the same as Richard and Israel - he's just not quite right yet.
"They'll be ready for next week. We've got a big occasion before then we need to win.
"They'll be ready if we do the business against Argentina."
Muliaina - who made his All Blacks debut in 2003, captained the team in three Tests in 2009 and has scored 34 Test tries - is set to become the second New Zealander to reach 100 caps, following McCaw to the milestone.
Henry said: "He's been a great servant to New Zealand rugby. He's a world-class full-back who has been a very key member of this side for a very long time.
"He's always had a lot of ability. He's played some outstanding matches.
"It's a special occasion for him and he deserves the honour."
Following four comfortable victories in the group stages, Henry knows his side must now raise their game.
He added: "It's a huge step up. Argentina always cause major difficulties.
"They played England in the first game and could've won that game.
"They're always a very competitive side. Their pack drives well, scrums well, is good at the breakdown. It will be a difficult game.
"They'll be very competitive. They always give France a good game.
"We're expecting a big game."
Aaron Cruden, who was called into the All Blacks' squad to replace Carter, has been named on the bench.
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