The injury means Carter will miss the All Blacks' Rugby Championship opener against Australia in Sydney on Saturday, most likely the return clash in Wellington a week later and possibly the following Tests with Argentina and South Africa as well.
The 31-year-old will be replaced by Aaron Cruden and Carter admitted the injury came as a big blow, occurring only a couple of days after the announcement he was taking a six-month sabbatical later this year.
"It's a bit frustrating, especially when the body feels good and then you have a wee setback like this," Carter said.
"So it's always frustrating but, the thing is, I've had injuries like this before so I know what I have to do to get back playing and play as well as I know I can."
All Blacks coach Steve Hansen rejected claims the injury could bring forward Carter's break, and is confident the No 10 will play some part in their Rugby Championship campaign.
"I don't think we need to be too keen on getting rid of him. We'll see how he goes over this period," he said. "The scans show it's not a biggie, it's something that's a nuisance more than anything else.
"Aaron is ready to rumble. He's also played a couple of Tests this year and understands what we're trying to do. He's part of the leadership group so it's business as usual."