Hedman left Thursday's 5-1 loss to Calgary after he was hit on the side of his left knee in a collision with Flames right winger Garnet Hathaway.
"When I guy can't really put weight on his leg, and doesn't come back, it didn't look very good," captain Steven Stamkos said after Thursday's game. "Stuff happens. You can't control it. You can't replace a guy like [Hedman]. He's one of the top three defensemen in the league, and a huge part of this team."
The 27-year-old Hedman, who finished third in Norris Trophy voting last season, has posted six goals and 27 assists in 44 games this season.
Hedman is third among defensemen this season in scoring, and he's leading the NHL in plus/minus at plus-24. He's averaged 25:36 time on ice per game, which is more than four minutes more than any other Tampa Bay player.
The injury means Hedman will likely miss the NHL All-Star Game, scheduled for Jan. 28 in Tampa, after being named to the Atlantic Division squad this week. Potential replacements include Boston Bruins rookie defenseman Charlie McAvoy, Toronto Maple Leafs defenseman Morgan Rielly and Hedman's rookie Lightning teammate, Mikhail Sergachev.
ESPN's Greg Wyshynski contributed to this report.