If he gets back for the playoffs, though, O'Neal is promising to make up for his time out.
O'Neal will miss about eight weeks, the team said. He was examined Sunday by specialist Dr. Thomas Graham at the National Hand Center in Baltimore, who performed the surgery Monday morning.
"He feels like he let us down, but we understand injuries happen in the game," said teammate Jamario Moon, who, along with the other Cavs, got a text from the star center. "I think he's really down about being out. ... He let us know it's time to continue playing basketball and he's going to be all right."
The recovery timeline means O'Neal, who turns 38 on Saturday, may not be ready for the start of the playoffs April 17. The Cavaliers acquired him last summer with an eye toward the postseason, after Dwight Howard and Orlando eliminated them in the Eastern Conference finals.
Cleveland enters its game Monday against the Knicks leading Orlando by six games for the best record in the East. Should the Cavaliers and Magic retain the top two seeds, they wouldn't meet until the Eastern Conference finals, which begin in mid-May.
"Will be out for a min but when I return it is on," O'Neal posted on his Twitter account Monday morning. "Win da ring for da king! Luv my team, Cavs baby!"
O'Neal has played well for the Cavaliers, averaging 12 points and 6.7 rebounds in 53 games. He injured the thumb Thursday at Boston when his shot was blocked by Glen "Big Baby" Davis with just over 7 minutes left in the first half.
Cavs general manager Danny Ferry said O'Neal will wear a splint for the next two weeks, then begin his rehab.
"Our guys have done a very good job of stepping up this season. We are confident they will do the same in this situation," Ferry said. "We are fortunate to have some depth in our front court that can keep us moving forward while Shaq recovers and returns to play for the postseason."
Former backup Zydrunas Ilgauskas, traded to Washington for Antawn Jamison, is now a free agent following a buyout by the Wizards. Ilgauskas is free to sign with any team, but will have to wait another couple of weeks under NBA rules should he elect to re-sign with the Cavaliers.
Cleveland has battled injuries and personnel losses all season.
Point guard Mo Williams recently returned after missing 11 games with an injured shoulder and guard Delonte West bounced in and out of the rotation early because of personal reasons. Powe debuted last week after recovering from knee surgery last summer.
"There's nothing we can do about it," coach Mike Brown said. "It's happened all year. Hopefully someone will step up and fill the void and we'll just keep moving forward."