An MRI scan showed damage which requires at least six weeks out of the game, according to medical staff.
The league leaders' next match is against the Lions at AMI Stadium in Christchurch on April 12, but Deans will not hurry Brett - set to return to training after a shoulder injury - into action.
Deans may also consider versatile international Leon MacDonald, who has started at Test level at fly-half, or handing a first start to Hamish Gard .
"We won't be rushing him in before he's ready. Leon's a possibility. There's a whole lot of things we can look at, really," Deans said.
The new Australia boss also felt his side could cope with losing Carter, and that the player had the mental resolve to mount a successful return.
"We'll just keep trucking on," Deans told The Christchurch Press.
"It's bad luck for DC, and no-one likes to see a player suffer like that, but it's just part of the territory.
"He's in great shape mentally. Now, he's got the chance to get himself back in better shape.
He added: "Potentially, he could be out for longer but it's just a matter of seeing how the ankle responds over the next few weeks."
At international level, the injury puts Macdonald and Blues' Nick Evans in pole position for the All Black number 10 shirt for the opening match of the season against Ireland on June 7.