The high-scoring center is expected to return to Tampa on Thursday to begin rehabilitation. A timetable has not yet been set for his return.
One of the team's trainers stayed with Stamkos at the hospital and was set to meet with doctors at the end of Tuesday to go over the rehab protocol that will follow the surgery.
Lightning general manager Steve Yzerman spoke briefly with his franchise player Monday evening.
"In the brief period that I did speak with him, I guess not surprisingly if you know him, but particularly upbeat. He said, 'You know I'll come back stronger than ever.' So all things considered, he was in good spirits," Yzerman said.
Yzerman also is the executive director of the Canadian Olympic team.
"In regards to the Olympics, we'll wait and see," he said. "I don't have a time frame on how long he's going to be out. I do know when they tell me it's going to be a pretty broad range so I expect him, again knowing him and being young, he'll be on the shorter end of the rehab process."
Stamkos was injured Monday with 7:11 remaining in the second period of a game at Boston. He was taken off the ice on a stretcher after crashing into the post.
Stamkos was backchecking on a play when he got tied up with Bruins defenseman Dougie Hamilton. The pair went into the net hard.
ESPN.com's Scott Burnside and The Associated Press contributed to this report.