Green had surgery at the Cleveland Clinic. The Celtics said earlier that the procedure should repair the condition, but Green will miss the remainder of the 2011-12 season.
Celtics head coach Doc Rivers said after practice Monday that Green's surgery "went well" and hoped the next bit of news they received would be "that he'll be able to play again."
"That would be terrific," said Rivers. "I don't care if it's with us. I want it to be with us, obviously. I just want him to be able to fulfill his life. Really, at the end of the day, that's what we want."
The Celtics acquired Green from Oklahoma City last February in the trade that send Kendrick Perkins to the Thunder. He averaged 9.8 points and 3.3 rebounds in 26 games for the Celtics, and has career averages of 13.9 points and 5.5 rebounds in four seasons.