Citing an unnamed source, the Pittsburgh Post-Gazette reported the surgery is to repair damage that impeded his performance in the post-season.
The 2014 Hart Trophy winner is not expected to miss any time next season, according to the report.
The newspaper added that Crosby decided to have the operation only after therapy failed to correct the problem.
Crosby won the NHL's regular-season scoring championship with 104 pointslast season, but managed just one goal and eight assists in 13 playoff games.
Crosby consistently denied during and after the playoffs that he was playing injured.