Coach Ian Foster said he had made a replacement decision, but because of different flights to London for the next game against Wales, he had not been able to discuss that with the player to take on the role and would release the captain's name once he had done that.
Billy Harmon from the All Blacks XV will replace Cane.
Hooker Dane Coles also will return home after he scratched from the game minutes before kick-off when a calf muscle tightened up. Asafo Aumua will replace him.
Back-up players from the All Blacks XV lock Patrick Tuipulotu and utility back Damian McKenzie will rejoin the All Blacks XV to play Ireland A, while Mark Telea will have another week with the All Blacks at least.
It was later announced Leicester Fainga'anuku was returning to the side in Wales after he left the team in Japan for family reasons.
Foster said it was disappointing to lose two of their leaders in Cane and Coles, especially after the first game, but it was another adjustment the All Blacks have had to keep making.
"It will creates a great opportunity for the likes of a Dalton Papali'i and he's in good form. It's the reality of rugby, you always want to get through your first couple of games injury free. It hasn't worked out this way, and it doesn't change the challenges coming up."
Foster said the lineout did not function well against Japan, and opportunities were missed, while the transition defence looked slow to move and not connected.
"There are critical areas where I don't think we were up to par, but it was also a pretty good Japan team we played against and particularly that transition defence is a strength for them. They feed off the scraps and did it well. We knew that was coming, and we weren't quite quick enough."
However, they had the win, and it was a good building block and would provide plenty to talk about in their Monday review. He thought there were timing issues that reflected the time out of playing the game and some execution errors.
He said he was confident they could get their lineout back to the strength it had been for the side this year, and it had been a little bit of an upper-cut to them in that area that they couldn't impose their game.
"So much pressure, and points, now come from that facet of the game, especially when you get into the attacking 22m area, and to miss two or three lineouts in that space was disappointing and not something we seek to do.
"In the first half, especially at 21-3, it stopped us from pushing on, and we've got to get more efficient. We'll roll up our sleeves and get in some good work."
In relation to lock Brodie Retallick's red card for dangerous play, Foster said they would enter into the judicial process by presenting a rugby case and see what unfolded. The hearing is likely to be on Tuesday.
Wales was a side that looked to have more ambition about how it wanted to play, he said.
Wales would be a different team from that they struck last year when the All Blacks caught them on the hop.
Playing at Millennium Stadium, they knew what to expect, he said. Wales would be physical, and looking to play at speed, while the All Blacks would want to go up a couple of cogs from their Japan effort.