The Lightning confirmed the injury on their official Twitter account, just hours after Stamkos was taken off the ice on a stretcher.
Lightning general manager Steve Yzerman announced later Monday that the 23-year-old Stamkos, the NHL's co-leader in goals and points, will undergo surgery. The operation is expected to take place Tuesday.
"The medical staff in Boston, in consultation with our team physicians, has made the decision to surgically repair the injury," Yzerman said in a team release. "The procedure is expected to take place tomorrow morning.
"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."
Stamkos reached out on Twitter later Monday.
Thanks to all my family, friends, and fans for all the well wishes! I will be back as soon as possible !!
— steven stamkos (@RealStamkos91) November 11, 2013
Lightning coach Jon Cooper acknowledged that the long-term absence of Stamkos will be difficult for Tampa Bay to overcome.
"It's obviously tough to see him go down, not only for our team -- he's one of the best players in the world," Cooper said following Tampa Bay's 3-0 loss to the Bruins. "People come out to cheer the Boston Bruins here, and they come to see Steven Stamkos play hockey. It's a loss for everybody."
Stamkos was backchecking on a play late in the second period when he got tied up with Boston defenseman Dougie Hamilton, and the pair crashed hard into the Bruins' goalpost.
Stamkos' left skate appeared to hit the post first before his right leg crashed into it around the shin area. He tried to get up twice before going down to the ice in pain, immediately grabbing his leg just above the ankle and rolling on the ice in agony.
"It's just an unfortunate play," Hamilton said. "I was just trying to drive the net, and he was too fast for me. I think he caught me and we both just went to the net.
"I don't know what happened -- he fell and hit the post pretty hard. It's unfortunate and kind of sad to see that happen."
A stretcher was brought out after a brief delay, and Stamkos was taken off to loud applause at TD Garden. As he was carted away, Stamkos put both hands to his face in apparent pain.
"It's definitely a big loss," Lightning center Nate Thompson said. "When someone goes down, everyone else has to step up. Obviously, you can't replace a guy like Steven Stamkos. But as a group, we can come together and lift him up because he's done a lot for this organization."
A two-time All-Star, Stamkos has 222 goals and 187 assists in parts of six seasons, all with the Lightning. The No. 1 overall draft selection in 2008, he has led the NHL in goals in two seasons.
ESPNBoston.com's Joe McDonald and The Associated Press contributed to this report.