The procedure to Crosby's left wrist was performed by Dr. Robert Hotchkiss of New York, in collaboration with team physician, Dr. Dharmesh Vyas of UPMC.
The 34-year-old center will miss the start of training camp and is expected to be sidelined for a minimum of six weeks.
"This is not a new injury for Sid. It is something that he has played through for years," said Penguins general manager Ron Hextall. "After exhausting all minimally-invasive options and much discussion, it was decided that surgery was in his best interest."