George Bailey remains stand-in skipper of the one-day team.
Clarke's career is uncertain, with the 33-year-old on Saturday revealing fears he will never play again.
CA is continuing to consult with specialists over the best way to treat Clarke's latest injury.
"There was a strong argument for Brad to assume the captaincy until Michael returns," chief selector Rod Marsh said.
"But given we don't know how long that will be, we felt the time was right to take a longer-term view and give a young player this chance.
"Brad Haddin has done an exceptional job as vice-captain since assuming the role last year and will provide strong support to Steve just as he has done for Michael."
Smith debuted as a leg-spinning allrounder at age 21, but cemented his spot in the side as a dependable batsman over the past 18 months.
The right-hander has scored 1490 runs at an average of 51.37 in 18 tests since earning a recall during Australia's woeful tour of India last year.
"He is an exceptional young man who is highly regarded by the national selection panel, not only for his fine performances with the bat but also his maturity and clear leadership potential," Marsh said of Smith.
Shaun Marsh will take Clarke's place in the side for the second test, which starts at the Gabba tomorrow.
But it is unclear who will bat at No4 in the absence of Clarke, with Smith charged with setting the order.
"I like batting as high as possible," Smith said after scoring an unbeaten ton on day two of the first test.
"I'll just keep batting and if I get a chance to move up the order, that will be great as well."
Steve Smith
*23 tests
*1749 runs at 46.03
*Australia's 415th test player and 45th test captain
*Last week's unbeaten 162 against India was highest test score
- AAP
