Smith said he would not join the squad heading to New Zealand for the three-match series starting on Jan. 30 having suffered strained medial ligaments in his left ankle.
"It's a bit of a shock," Smith told reporters in Adelaide. "I just landed really awkwardly on my foot and I felt something straight away. I was a little bit concerned, I've never really injured my ankle like that."
The 27-year-old added that team medical staff informed him he could resume training in seven to 10 days but the injury was not serious enough to rule him out of the four-match test series in India starting in Pune on Feb. 23.
Smith will undergo a scan on the injury but expects to attend a training camp in Dubai ahead of the tour of India.
"They think it's just a medial ligament sprain but I'm having an MRI ... to see if there's any more damage," he said. "I'm confident I'll be fine to train in Dubai after that and for the first test in India."
Vice-captain David Warner is being rested for the New Zealand tour and selectors had discussed reinstating the left-handed opener with Smith being ruled out.
"We made the decision that it was in his best interests and in the best interests of the team that we continued with our original plan to give him a break for this series," interim chairman of selectors Trevor Hohns said.
"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."
Wade said he was excited by the opportunity.
"Being asked to captain Australia is obviously not something I was expecting and it is still sinking in, but I am hugely honoured by the decision ...and very excited about it," said the 29-year-old.
Following the series-opener in Auckland, the teams play further matches in Napier on Feb. 2 and Hamilton on Feb. 5.
(Writing Simon Jennings in Bengaluru/Sudipto Ganguly in Mumbai; editing by Greg Stutchbury)
