Couturier was skating in on goal when his right leg was hit by defenseman Radko Gudas, who was moving backward and didn't see Couturier.
After tumbling to the ice, Couturier threw his stick against the boards in anger. He was assisted off the ice.
Flyers general manager Ron Hextall said the team will update Couturier's condition on Wednesday.
The Flyers trail the Pittsburgh Penguins 2-1 in their best-of-seven first-round series. They play again Wednesday in Philadelphia.
Couturier leads the team in postseason scoring with a goal and two assists.