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.
Stay Connected
NHL.TV™
NHL GameCenter LIVE™ is now NHL.TV™.
Watch out-of-market games and replays with an all new redesigned media player, mobile and connected device apps.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads