Lightning GM Steve Yzerman says his star centre will undergo surgery Tuesday morning to repair the injury.
"The biggest concern for me, and the rest of the Lightning, is that decisions are made in Steven's best long-term interest, and we feel this is the appropriate course of action," Yzerman said in a release.
It's bad news for the Lightning and for Canada's Olympic team. Stamkos was considered a lock to represent Canada at the 2014 Sochi Games but the injury puts his status in doubt.
"Obviously he's a big part of our team," Lightning veteran Marty St. Louis said.
The team's leading scorer and one of the top players in the league, Stamkos was backchecking on a play late in the second period Monday when he got tied up with Boston defenceman Dougie Hamilton. The pair went into the net hard, Stamkos's leg smashing hard against the post.
Stamkos immediately grabbed his right leg and was rolling on the ice in pain.
"It's obviously tough to see him go down, not only for our team, he's one of the best players in the world," Tampa Bay coach Jon Cooper said. "People come out to cheer the Boston Bruins here, and they come to see Steven Stamkos play hockey. It's a loss for everybody."
After a brief delay, a stretcher was brought out and he was taken off to loud applause. As he was carted off, he put both hands to his face in apparent pain.
Stamkos entered the day tied for the league lead in scoring with 14 goals and nine assists.
— With files from The Canadian Press