A source told Sporting News a disciplinary hearing would not be held.
Connolly was chasing the puck into the corner when he was hit by Richards, and spent about two minutes on the ice before skating slowly to the dressing room.
Richards was assessed a two-minute boarding penalty on the play.
Connolly has a history of injury problems, including several concussions. One of the concussions forced him to miss the entire 2003-04 season.
Connolly will not play in Game 7.
Information from The Associated Press was used in this report.