Australian team doctor Trefor James said the surgery in Adelaide had been successful.
"The injury was not as extensive as had been anticipated and he will be able to resume playing sooner than had been initially expected," he said in a CA statement on Friday.
The South Australian tearaway pulled out of the Australian One-day team for this week's Super Series against the World XI and an initial diagnosis was that he could be sidelined for up to three months and out of all of Australia's home Tests against the West Indies and South Africa.
Tait will undergo a rehabilitation program in Adelaide where his progress will be closley monitored, CA said.
CA did not say when Tait would resume playing cricket.