The 26-year-old Cane was visibly in pain and the All Blacks later said he had suffered a fracture in one of his neck vertebrae although there was no nerve damage. He had surgery and was expected to remain in South Africa for another week.
"Like any fracture it takes a couple of weeks and months," All Blacks doctor Tony Page said. "It will probably take about three months for the bone to get strong but we'll just take it step-by-step.
"The operation is really just to keep everything in the right place so the bone can heal on its own accord."
Cane was expected to be out of action for at least three months, but Hansen said they would not hurry his return to the field with an eye on next year's Rugby World Cup.
"It is expected he will make a full recovery and be back playing," Hansen added. "Once you remove the drama of it being a neck injury you've just got to look at it and treat it like any fracture."
Cane's absence from the end-of-year tour will test Hansen's depth in the number seven jersey, with Savea expected to become the starter after a superb performance against the Springboks.
Canterbury Crusaders' Matt Todd is the only other specialist number seven in New Zealand with test experience, but was overlooked for the Rugby Championship squad after he took up a short-term contract in Japan that runs until early next year.
Otago Highlanders' Dillon Hunt played a non-test match against a French XV on last year's end-of-season tour, while the Wellington Hurricanes' Gareth Evans was impressive in Super Rugby this year and was mentioned as a potential dark-horse pick for the Rugby Championship squad.
Hansen, however, will have plenty of opportunity to mull his choices with his decision to select an extended squad of players for their two tests in Japan before they head to Europe.
The All Blacks face Australia in the third Bledisloe Cup clash in Yokohama on Oct. 27 before they face Japan on Nov. 3 in Tokyo. They then meet England at Twickenham on Nov. 10.
Hansen said a large group of players would then head to London after the Wallabies test, with the remainder staying behind to prepare for the Japan match.
(Reporting by Greg Stutchbury; Editing by Ken Ferris)
