Palat played one shift to begin the third period before leaving with the score tied 2-2.
The Canadiens won the game 5-4 in overtime.
Palat missed the final game of the Lightning's regular season Sunday with an injury after putting together one of the best seasons of any first-year player in the NHL with 23 goals, 36 assists and a team-leading plus-32 rating in 81 games.
Lightning coach Jon Cooper did not have an update on Palat's condition after the game. Tampa Bay will host Game 2 on Friday (7 p.m. ET, CNBC, FS-F, CBC, RDS).
"I feel bad for that poor kid," Lightning coach Jon Cooper said. "He goes 80 games or so without getting dinged up, and he keeps getting dinged up."