Carter had the surgery in Melbourne, Australia on Monday and flew back to New Zealand on Wednesday, the union said in a statement.
The All Black No 10 was ruled out of the Rugby World Cup when he tore his left adductor on October 1, the day before New Zealand's pool match against Canada.
Carter said in the statement today the surgery to repair the tendon "went well" and he will now be concentrating on his rehabilitation. He will undertake a "graduated rehabilitation programme" involving strengthening exercises which aims to have him walking, then running within eight weeks.
Carter said he hopes to be fully recovered within 12 weeks.