Stillman, one of the Hurricanes' top scorers in their run to their first Stanley Cup, is expected to take up to four months to recover, team president and general manager Jim Rutherford said.
Rutherford didn't know how Stillman injured his shoulder but said during recent weeks it became evident that the injury wouldn't heal as quickly as he hoped.
"We had hoped that it would rehab over time and be ready for camp," Rutherford said. "But it didn't. It was more serious than just rehabbing."
Stillman's agent, Rick Curran, did not immediately return a phone message seeking comment.
Stillman tied for second on the team with 76 points (21 goals, 55 assists) and became only the sixth player in NHL history to win the Cup in two straight seasons with different teams. Stillman, who won with Tampa Bay in 2004, ranked second in the playoffs with 26 points.
Rutherford said he hopes some of the Hurricanes' offseason additions can fill in for Stillman. Carolina bolstered its scoring depth by trading for forward Scott Walker and signing forwards Jesse Boulerice and Shane Willis.
"Anytime you lose a player like Cory, you don't just replace him," Rutherford said. "This is where other players have to pick up a little slack, and it gives other players an opportunity.
"We have more quality forwards than the start of last year. We hope that other players step up and fill the gap," he added.
The Hurricanes open the season Oct. 4 against Buffalo.