The wicketkeeper had told reporters in Napier earlier on Wendesday that he had already been ruled out of the second one-dayer at McLean Park, but hoped to be able to play in Sunday's third game in Hamilton.
"With Matthew not being fit for Thursday's game... it has been decided to send him home for an assessment and treatment in Melbourne, with a view to him being fit for the tour of India and the training camp in Dubai that precedes it," Cricket Australia's (CA) chief medical officer John Orchard said.
"We are hopeful this injury will settle down relatively quickly and that he will be able to participate in that tour without any issues."
Aaron Finch will continue to lead the side, having stepped in about 30 minutes before the first game started in Auckland on Monday.
Wade had been appointed to lead Australia in the absence of regular skipper Steve Smith (injury) and rested vice-captain David Warner.
CA said they would not seek a replacement player.
Peter Handscomb took the gloves for the Eden Park match and is to continue behind the stumps for the rest of the series led 1-0 by New Zealand.
Wade, who looked uncomfortable doing wicketkeeping drills with assistant coach Brad Haddin on Wednesday, said the injury had occurred at training when he dived for a catch and felt his back "tighten up".
"It's just about trying to rest and recover," Wade told reporters at McLean Park. "It has been really frustrating. But there should be no problem for India."
He later said facing a bus ride on Friday to Hamilton for the third match had been a factor in the decision to return home.
"It's not a major injury but with the short turnaround between matches and the four-and-a-half hour journey by bus to Hamilton for the next match, its been decided its best for me to go home and get some treatment in Melbourne," Wade said.
"I'll get that bit of treatment in Melbourne and we're hopeful it'll be fine by Sunday or Monday and I can be on a flight to Dubai and start training pretty much as soon as I hit the ground there."
The four-test tour of India starts in Pune on February 23.
First Published: February 1, 2017, 10:17 AM IST