Clarke's decision to go under the knife has ensured he will definitely miss the three remaining test matches against India and possibly the 50-over World Cup, starting in mid February.
Cricket Australia team doctor Peter Brukner said in a statement on Monday that the 33-year-old's injury was "substantial" and it was too early to say when he may be able to make a comeback.
"Whilst surgery is not always required with hamstring injuries, Michael has substantial damage to a key part of the hamstring tendon and it was felt the best course of action was to surgically repair the damaged area," said Brukner.
"His recovery and the timing of his return to play will be dependent on the surgeon's advice and how well he recovers in the coming weeks."
Clarke injured his hamstring while fielding during Australia's first test win over India on Saturday. He also suffered back pain while batting in the first innings, forcing him to retire hurt before he returned to complete a century.
They were just the latest in a series of chronic problems he has had with his back and hamstrings over the past two years and prompted him to speculate that he many never play again.
Cricket Australia announced on Monday that Steve Smith would take over as the new test skipper, but no decision had been made yet on the one-day team.
George Bailey is the current vice-captain and has filled in for Clarke before whenever the skipper has been sidelined.
"The next 24 to 48 hours will give us far better guidance on that process. But I think George Bailey has done a fantastic job,"
Australian team performance chief Pat Howard said. "We're number one in the world. He's led the last two series, so all that was discussed."
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