The forward sustained an undisclosed injury in Game 1, a 5-1 win Monday.
"He's day to day in the series," Tampa Bay coach Jon Cooper said after the morning skate Wednesday. "It's very much like [the Steven] Stamkos (injury) situation last year, I'll let you know when he's going to play, but he'll be out tonight."
Forward Mathieu Joseph replaced Killorn. Joseph last played in Game 3 of the Stanley Cup First Round against the Florida Panthers.
Killorn plays on the second line with Stamkos and Anthony Cirelli, is on the top power-play unit and part of the penalty kill for Tampa Bay.
"He brings immense value and I can have this conversation about all 20 guys in different ways," Cooper said. "Alex is a piece to the puzzle. He plays multiple special teams, he kills penalties for us, he's on the top power-play unit, he can check for us, he chips in on the goal-scoring side of things. He's a depth veteran player you can depend on game in and game out.
"When you win a hockey game, he's contributed in a way that he doesn't always get his picture in the paper. Key part to our team, but it's the playoffs, guys are in and out. You lose guys all the time. It's part of it, and for tonight we're going to have to play without him."
Killorn didn't play during the final 19:04 after playing one shift of 23 seconds in the first minute of the third period Monday. He appeared to be in pain after sliding to block a slap shot by Montreal defenseman Jeff Petry with his left leg at 13:32 of the second period.
He was able to skate to the bench under his power before falling over the boards into the bench area. He stayed on the bench and went back on the ice to skate around during the next timeout.
Killorn played two more shifts in the second period, neither lasting longer than 24 seconds, and one shift in the third before leaving the game.
"'Killer' is a big part of our team, eats up a lot of minutes and plays in every situation," Tampa Bay forward Tyler Johnson said. "It's going to be everyone having to step up in different roles. That's the great thing about our team, though, is we have that depth and it's going to take everybody."
Killorn was fourth on the Lightning with 17 points (eight goals, nine assists) in 19 postseason games. He was averaging 17:32 of ice time per game, including 2:34 on the power play and 1:38 on the penalty kill.
