Lee hit Backstrom early in Game 1 of the first-round playoff series, after which Washington blue-liner John Carlson immediately came to his teammate's defense.
The officials assessed Lee an interference minor for the hit and also gave both Lee and Carlson roughing penalties.
Later in the period, Capitals agitator Tom Wilson dropped the gloves with Lee.
Backstrom initially played through the hit, remaining on the ice for nearly a minute of game time afterward and then logging five more first-period shifts.
However, he didn't emerge for the start of the second frame, and the Capitals later ruled him out for the rest of the contest.
Washington head coach Todd Reirden said postgame that the talented pivot was scheduled to be evaluated Wednesday night, and there will be an update on his status Thursday, according to NHL.com's Tom Gulitti. Capitals captain Alex Ovechkin said he believes Backstrom will "be fine."
Backstrom ranked second in assists among Washington skaters (42) and third in points (54) during the regular season.