Hedman will have surgery Tuesday and is expected to need up to four weeks to recover. He was injured in a 3-1 loss to the Columbus Blue Jackets on March 30.
"He has been playing through that even since," Lightning general manager Julien BriseBois said Tuesday. "He is having a meniscectomy today. Expected down time is 2-4 [weeks], so we're not concerned going forward."
Hedman missed the final two games of the regular season before scoring 18 points (two goals, 16 assists) and leading the Lightning in average ice time (24:42) and blocked shots (48) in 23 playoff games to help them win the Stanley Cup for the second straight season.
Hedman was among a number of Lightning players who played through injury, though BriseBois said none are expected to miss the start of next season.
Forward Barclay Goodrow and defenseman Ryan McDonagh each played the postseason with a broken hand. Goodrow scored six points (two goals, four assists) and tied for second on the Lightning with 68 hits in 18 postseason games. McDonagh had eight assists in 23 games and was second on Tampa Bay in ice time per game (22:50) and blocked shots (46).
Nikita Kucherov, who led the postseason with 32 points (eight goals, 24 assists) in 23 games, sustained a broken rib in the semifinals against the Islanders. The forward did not miss a postseason game after not playing in the regular season because of offseason hip surgery.
"Played with a flak jacket from that point on and also had a nerve block injection the day before every game from that point on," BriseBois said. "It makes his performance during these playoffs both before the injury and post-broken rib all the more impressive. He's a tough hockey player, he's an incredible hockey player, and all of us in Bolts Nation are happy he's our 'Kuch'. I couldn't be happier for him and he seemed really happy that we won as well. There isn't a more determined player out there than Nikita Kucherov."
Alex Killorn missed the final five games of the Stanley Cup Final after the forward was injured in Game 1 against the Canadiens.
Tampa Bay defeated the Florida Panthers in six games in the best-of-7 Stanley Cup First Round, the Carolina Hurricanes in five games in the second round, the New York Islanders in seven games in the Stanley Cup Semifinals and the Montreal Canadiens in five games in the Stanley Cup Final.
"We had a number of players with some banged up shoulders, nothing of concern going forward," BriseBois said. "Obviously Alex Killorn suffered a broken fibula in Game 1 of the Stanley Cup Final. I saw the X-ray, it was broken in two very distinct pieces all the way through. Blocked that shot, broke his leg on Monday. On a Thursday, in hopes of coming back and helping us win a Stanley Cup, had a rod inserted in his fibula and was skating by Saturday.
"That's how you win a Stanley Cup."
NHL.com independent correspondent Corey Long contributed to this report