Team doctor Tony Page confirmed Cane, who has featured in 60 Tests, would need to undergo surgery and was facing at least three months out.
The 26-year-old appeared to suffer the injury following a collision with Springboks forward Francois Louw in the All Blacks’ 32-30 win.
Cane is set to be absent for the third Bledisloe Cup clash against Australia later this month as well as the four November Tests against Japan, England, Ireland and Italy.
“He was injured late in the first half,” Page explained to reporters.
“He’s got a small fracture in the lower part of his neck, on the right side, through one of the joints. This will need to be stabilised.
“Following that [surgery], he will stay in Pretoria for the week and we will keep an eye on him.
“He’s got to get through the operation, we’ve every confidence that he’ll do well with that, then, like any fracture, it takes a couple of weeks and months. It will probably take about three months for the bone to get strong but we’ll just take it step by step.
“Many sportsmen have had this injury and people in other walks of life, and they usually make a good recovery as it’s one level of the neck.”
All Blacks head coach Steve Hansen also stressed that he expected to see Cane return at some point in 2019.
“It’s expected he’s going to make a full recovery and be back playing,” he added.
Sign up to our mailing list for a weekly digest from the wide world of rugby.Sign Up Now