The successful procedure was performed by Dr. T.O. Souryal of Texas Sports Medicine. Dampier is expected to make a full recovery.
It's uncertain whether the 6-foot-11, 265-pound center will remain with the Mavericks. His $13 million contract for next season is not guaranteed and could be attractive as a trade chip.
If a team trades for Dampier, it could waive the 14-year veteran to gain salary cap space, allowing him to become a free agent.
Dampier has played the last six seasons with the Mavs. He averaged 6.0 points and 7.2 rebounds in 55 games last season. He missed time with an open dislocation on his right middle finger.
The Mavericks were the second seed in the Western Conference playoffs but were knocked out by the San Antonio Spurs in the first round.