All Black star Dan Carter has undergone surgery following his World Cup-ending groin injury, the New Zealand Rugby Union (NZRU) said in a statement.

In an NZRU statement Carter said the surgery, which he had in Melbourne on Monday before returning to Auckland on Wednesday to repair his left adductor longus tendon had "gone well".

The flyhalf, whom many New Zealand fans considered central to their team's hopes of winning the World Cup, was ruled out of the remainder of the tournament after suffering his injury during kicking practice on the eve of the All Blacks' final pool match against Canada.

Test rugby's all-time leading points scorer, with 1,250 from 85 matches, the 29-year-old Carter will now embark on a rehabilitation programme the NZRU said would "involve re-establishing normal walking with strengthening exercises, with a view to progressing onto running and kicking over an eight-week period".

The NZRU statement added Carter hoped to be "fully recovered" by about the 12-week mark.

Hosts New Zealand's World Cup campaign has been beset by injury problems, with Carter's stand-in, Colin Slade, also being ruled out of the tournament with a groin problem suffered during their quarterfinal win over Argentina.

That has left third-choice Aaron Cruden in the pivotal flyhalf position for this weekend's semifinal against Australia at Eden Park.

But the good news for New Zealand fans desperate to see the team win only its second World Cup title since the country staged the inaugural 1987 edition was that captain and Richie McCaw was named in coach Graham Henry's team to play the Wallabies here on Friday, even though the inspirational flank has been nursing a longstanding foot problem throughout the tournament.

Carter, speaking earlier this month, before his operation but after his dreams of World Cup glory were dashed following his role in New Zealand's failed campaigns of 2003 and 2007, insisted he'd no history of groin trouble.

"After kicking a ball it just popped and I went down on the ground in agony," Carter, widely acclaimed as the world's best flyhalf, said.

"Just the pure randomness of the injury and for it to come out of the blue, my body was really good leading into the week and it was good all week and I haven't had any groin or abductor or hip problems in the past.

"So for something like this to happen is really tough. I can't put my finger on why and I'm constantly asking why did this happen and I don't have the answer."