In the third quarter of the Warriors' 119-116 road loss, Nurkic had his hand on Green's hip while defending him when Green swung around wildly, hitting Nurkic with his open hand.
Green received a 'Flagrant Foul 2' and was ejected for making "unnecessary and excessive contact to the face," the referees determined after a video review.
The league said it took into account Green's history of "unsportsmanlike acts" and that he would be required to meet certain league and team conditions before he returns to play.
Green previously served a five-game suspension in November for an altercation with Minnesota's Rudy Gobert and sat out Game Five of the 2016 NBA Finals for committing a flagrant foul on Cleveland's LeBron James in the prior game.
The Cavaliers won Game Five and went on to win the series.
A four-time NBA champion and All Star, Green has played a crucial role in building the Warriors dynasty in the San Francisco Bay Area.
He is the emotional leader of the team and his quick tempo and court vision helps creates shots for sharpshooting guards Steph Curry and Klay Thompson.
The Warriors (10-13) are 11th in the Western Conference and play the Clippers in Los Angeles on Thursday.
