Lightning General Manager Steve Yzerman said Stamkos suffered a broken right tibia during the Lightning's 3-0 loss to the Bruins.
"At this point Steven will be out indefinitely," he said. "The medical staff in Boston, in consultation with our team physicians, has made the decision to surgically repair the injury."
The GM said the procedure would be performed Tuesday.
The 23-year-old Stamkos, who is tied for the NHL lead in goals (14) and points (23), was carried off the ice on a stretcher after slamming his leg into a goalpost while tangled with Boston defenseman Dougie Hamilton.
"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.