The incident happened during Washington's 3-2 overtime win over Tampa Bay on Thursday.
About 11 minutes into the second period, Connolly was hit in the head by Green and stayed down on the ice for a bit, then was taken toward the locker room.
On the play, Capitals defenceman Dmitry Orlov had Connolly pinned against the boards when Green joined in and knocked Connolly down.
No penalty was assessed on the play and Connolly returned before the end of the period.
It's Green's second infraction in his seven NHL seasons.