Pocock, 24, suffered the injury playing in a Super Rugby game for the ACT Brumbies against the New South Wales Waratahs last weekend, and had already been ruled out for the British and Irish Lions' tour of Australia later this year.
There was further bad news for the Wallabies when Berrick Barnes sustained a suspected fractured wrist.
"I'm pleased to have the surgery out of the way," Pocock said in an ARU statement.
"Now I need to rest up and get myself ready to start the rehabilitation process. The key thing is that I'm patient and don't try to rush back.
"If that means season over, in terms of playing any more rugby this year, then so be it. Once I get into the rehabilitation, we'll see how it goes," added Pocock, who missed several months of rugby last year after suffering cartilage damage in his right knee.
Pocock, who has played 45 Tests since his debut in 2008, was one of four players to captain Australia last season as the Wallabies were hit by a catalogue of injuries.
Incumbent captain James Horwill has still not played since last May because of injury but the lock is expected to make his return for the Queensland Reds over the next few weeks.
Waratahs flanker Michael Hooper is the most likely replacement for Pocock in the number seven jersey after several impressive performances for Australia at the back end of last year.
Queensland youngster Liam Gill is also in fine form but Wallabies coach Robbie Deans may reconsider 110-cap flanker George Smith as an option.
Smith, 32, replaced Pocock for the Brumbies on Saturday, making his first Super Rugby appearance since 2010, but is still attached to his Japanese club and there are question marks about his eligibility.
Deans said last week that Smith would not be considered for the tests against the Lions in Brisbane, Melbourne and Sydney.
Versatile back Barnes, who has played for Australia at fly-half, full-back and centre, was hurt in the New South Wales Waratahs' Super Rugby encounter with the Cheetahs.
Barnes tackled giant lock Lodewyk De Jager midway through the first half and rolled away in agony, clutching his right wrist. He was replaced immediately by Rob Horne.
The 26-year-old Barnes, who made his 50th Test appearance against Wales in December, has only just returned to action from a knee problem.
The injury means Barnes he is likely to join Pocock on the sidelines for the three-Test series against the Lions.
- Sports & Recreation
- New South Wales Waratahs
- Berrick Barnes
- British and Irish Lions
- Super Rugby