All Blacks' Dr Deb Robinson said Carter's tendon was completely torn.
"He's had no history whatsoever of groin problems, he's had no symptoms on the day, he trained well ... and it just happened totally out of the blue.
"His scan, other than the current injury, is pristine, and for a guy who's played that much rugby and done that much kicking, that's quite remarkable.'
She said the injury usually involved a 10 to 12-week recovery period - well after the end of the cup tournament.
Mr Twaddle, the head of orthopaedic trauma at Auckland City Hospital, said an adductor longus tendon tear did not require surgery.
"It knits back in place and that particular muscle does very well after that kind of injury.
"It's like any muscle injury - initially painful, there'll be some bruising and then it'll settle down and it's likely to return to normal over time."
Recovery times varied greatly, Mr Twaddle said, but it would probably take four to six weeks before Carter could start doing increasing amounts of physical activity.
The 29-year-old fell and grimaced in pain during goal-kicking practice in Wellington on Saturday in preparation for yesterday's match against Canada.
Coach Graham Henry said the injury had ended Carter's World Cup, which was "devastating for Daniel".
"He's been a world-class player for a long time, probably one of the greatest players produced by this country."
Captain Richie McCaw has an ongoing foot problem but is expected to play through the cup tournament.
McCaw had surgery on his right foot in February to repair a stress fracture. A screw was placed in the fifth (outermost) metatarsal to reinforce the bone and he was expected to have recovered by now.
At the weekend, he described the injury as "a niggle".
Specialist foot orthopaedic surgeon Ali Bayan said stress fractures could take "sometimes months" to heal, particularly given the demands of top-level sport, but the screw should help.