"We have made the decision he won't be playing next week," Hansen said.
"The type of treatment he needs, it will take the pressure right off and give the calf the opportunity to come right.
"We're trying to, I guess, take him off his legs so he can concentrate on getting it better rather than trying to get it better to play."
Hansen said the early decision on his availability for next week had been made to give clarity to the team, and young fly-halves Aaron Cruden and Beauden Barrett, as they prepare for the Springboks in Dunedin.
Carter had been struggling with the injury as the All Blacks prepared for their match against Argentina in Wellington and was named on Thursday in the starting line-up.
He was later withdrawn from the team that defeated Argentina 21-5 on Saturday.
Hansen said the 30-year-old Carter, the world's leading points scorer, would be expected to travel with the team for their final two games in the Championship against the Pumas in La Plata on September 29 and against the Springboks in Soweto on October 6.
His omission was also about managing his fitness for the long term, Hansen added.
"He is getting older and the more you play the game, the more vulnerable you are to injury and he's got quite a few miles on the clock," he said.
"That's just standard for an older player and he has to be smart and we have to be smart about how we handle it.
"At the moment it's about getting him on the park now. It's about as much as that as it is long term.
"He's what we call a red flag athlete. He's high risk of getting re-injury so we have to be smart on the wear and tear of his body and how much pressure we put him under."
Hansen said it was "likely" Cruden would retain the fly-half position for the Dunedin test, which should boost the player's confidence after he failed to stamp himself on the game in the first half against the Pumas.
"He started off pretty average but the pleasing thing was he grew into the game," Hansen said.
"He's a young five-eighth (flyhalf) and it was really testing conditions and he will get a lot more out of that test match."