The 29-year-old was immediately withdrawn from the final Pool A encounter but it was hoped he would be fit for the knockout stages that begin with the quarter finals next weekend.
Carter's absence is the nightmare scenario for every New Zealand fan as their team look to win a first world crown since 1987.
"This was going to be his pinnacle and it's devastating for him," said All Black head coach Graham Henry, who had initially named Carter as stand-in skipper for the game against the Canadians following Richie McCaw's minor foot problem.
"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."
An injury to Carter during the quarter-final of the last World Cup against France coincided with their exit from the competition and media in the host nation are already suggesting a similar outcome could now be on the cards.
Carter's absence has affected the mood of the whole nation but All Black doctor Deb Robinson, who confirmed the extent of his injury, insisted the favourites' cup campaign would not be derailed.
"Dan has a significant groin injury. He has torn the left adductor longus tendon completely," said Robinson.
"He's not going to burst onto the finals and that's very sad. He's a key All Black, not only as the person who navigates the side on the field but also off the field.
"We need to move on and play the cards we've got. The group is shattered with this news, but they are also a resilient group."
Henry has called up Manawatu's Aaron Cruden to the squad and the 22-year-old Hurricanes playmaker will now compete with 23-year-old Colin Slade for the All Black No10 shirt for a likely last-eight tie with Agentina.