World Cup - Carter out of Rugby World Cup
The 29-year-old had been named captain for the All Blacks final Pool A game against Canada later on Sunday but had to withdraw from the team late on Saturday after sustaining the injury while practising his kicking at training.
"It has been confirmed he has a significant groin injury. He has torn the left adductor longus tendon completely," Robinson said at the team hotel.
Carter will travel to Auckland with the rest of the squad for further diagnosis but it was not yet clear if he required surgery, Robinson added.
Manawatu fly-half Aaron Cruden has been brought into the squad.
The loss of Carter is a huge blow because his back-up Colin Slade has produced mixed performances in his appearances to date and fans had been concerned that his lack of test experience was a gamble by the coaching staff heading into the tournament.
Carter's exit comes on the back of news that captain Richie McCaw, the only specialist openside flanker in the team, has been battling a nagging foot injury that forced him out of the Canada match and requires constant management.
Both players were considered integral to New Zealand's chances of ending a 24-year hoodoo at the World Cup, with Carter finding some of his best form as he challenged defensive lines with his running, distribution and kicking skills.
New Zealand have not won the Webb Ellis trophy since the initial tournament in 1987, despite entering every World Cup since as hot favourites to claim the title.
"It's devastating for Daniel," New Zealand coach Graham Henry said. "This was going to be his pinnacle and its devastating for him... this was his scene, this World Cup in New Zealand, and it was going to be his big occasion.
"I feel very sad for him but he is the type of guy who will handle this. He has strength of character... and I feel huge sympathy for him."
McCaw had ealier withdrawn from Sunday's match against Canada citing an ongoing foot problem.
McCaw, who will be replaced by Victor Vito for the match, said he decided to withdraw because of a "niggly" foot injury that forced him to miss part of this year's Super rugby season.
He had surgery in an attempt to fix the issue.
"My foot is a bit niggly. It's something I have managed all the way through," McCaw said. "If I had to play tomorrow in a knockout game I would have, but the decision was to make sure I'm right next week."
The All Blacks have already secured top spot in Pool A and a quarter-final berth with wins over Tonga, Japan and France. They will play the runners-up in Pool B, likely to be Argentina, in the quarter-finals next week.
"I probably could have played (against Canada) but it's the cumulative effect where it might take an extra day (to recover) because of the extra load I have had," McCaw said.
"You play at times with niggles every week, it's just the reality of every player, you play with those things.
"(But) there is a difference between (being) tough and playing because you're a bit sore and being stupid.
"At times you just play when you can do your job properly without doing anything silly. But there comes a point where you don't play because obviously you can't do your job."
The match will be the second McCaw has missed at the World Cup after he was a late withdrawal from the side to play Japan but he was confident he should be available for every game through the knockout phases.