The Lightning said Wednesday that Stamkos was out indefinitely, but coach Jon Cooper said the center would be back in time for the playoffs in April.
"If we put ourselves in a position to make the playoffs, he's going to be back," Cooper said Thursday. "And that'll be better than any trade deadline acquisition that anybody else is going to get.
"You've got to take your head out of the sand, dig your heels in and march on. And unfortunately, this has happened to us before and the guys have found a way."
TSN was first to report that Stamkos needed surgery.
According to the Tampa Bay Times, Stamkos clutched the back of his right knee after the collision and stumbled as he made his way toward the Lightning locker room. He did not return and there was little in the way of updates from Cooper after the Lightning's 4-3 victory.
Stamkos was off to a tremendous start to the season. His first-period goal Tuesday gave him nine goals on the season, and his 20 points are tied for third among all NHL players.
Stamkos missed all but one of Tampa Bay's postseason games last spring with a blood clot issue. But after signing an eight-year contract extension that pays him $8.5 million annually to remain with the Lightning, Stamkos returned in full health and played for Canada at the World Cup of Hockey.
Stamkos has collected points in seven of the past nine Lightning games, and Tampa Bay is tied for second in the Atlantic Division with Ottawa with a 10-6-1 record.
"You live in this reality now, and we've just got to have to face it," defenseman Victor Hedman said Thursday. "It'll be a good test for us. But at the same time, we know we can handle it, and we know we can win hockey games even though we're going to miss him."
Information from ESPN's Scott Burnside was used in this report.