It is not known if he will be ready for Friday's Game 1 of the Eastern Conference Final against Tampa Bay.
Backstrom left in the third period of Game 5 with the injury.
The Capitals captured the series, 4 games to 2, with a 2-1 overtime victory Monday night.
"To not have Nick in our lineup, you know, he's irreplaceable as a player," said goalie Braden Holtby. "Not any one single person can replace him; it takes a group effort and we knew that.
"I think that shows our true respect toward Nick, that we knew everyone was gonna have to step up, especially having Tom (Wilson) out. That shows that we're just, we stay in the moment, everyone's focusing on their job, what they can do to contribute to the success of our team. There's no selfishness in our locker room."
Wilson missed a third straight game while serving a suspension for his high hit on Pittsburgh's Zach Aston-Reese in Game 2.
Backstrom is third on the Capitals with 13 points (three goals, team-leading 10 assists) in the postseason.
Lars Eller took Backstrom's spot on the second line.
The Associated Press contributed to this report.