Smith's deputy David Warner was already due to be rested for the three one-day games in New Zealand starting Monday.
Smith was fielding in the fifth one-day international against Pakistan at the Adelaide Oval on Thursday when he injured his left ankle, CA said.
"He came off the field and had his ankle strapped and was able to return to the field for the remainder of the match," sports science and sports medicine manager Alex Kountouris said in a statement.
"Early indications suggest this will likely take seven to 10 days to recover, meaning Steve will be unable to (participate) in the Qantas Tour of New Zealand."
Wade said he was surprised but "very excited" to be chosen as Australia's 24th ODI captain by the national selection panel.
"With Steve Smith and David Warner absent it's an opportunity for me to captain the side for three matches," Wade said.
"But I'm not about to change too much and it's a case of trying to continue the disciplines that have earned us success in the recent past."
"Sam showed last summer what a talented player he is by averaging over 40 in his debut season at first-class level," CA interim selector Trevor Hohns said.
"He impressed again when playing for the National Performance Squad against A teams from Australia, South Africa and India in Townsville and Mackay during this past winter."
Smith's setback came less than a month before the tough India tour.
"We've got a lot coming up so they think it's an opportunity to rest it and be right for India," Smith told reporters in Adelaide, cricket.Com.Au reported.
"I'm confident I'll be fine to train in Dubai after that and for the first Test in India."
Hohns said it was in the best interest of Warner and the team to continue with the plan to rest the vice-captain for the New Zealand tour.
"That was our call and, that way, we will ensure David is fresh and ready to go in the build-up to the Test series in India that follows," he added.
The first Test against top-ranked India begins in Pune on February 23.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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