Smith will miss Game 4 of the series, which will played Sunday afternoon in Boston. The Knicks are up 3-0 in the best-of-even series after the 90-76 victory in Game 3.
Terry was guarding Smith, the NBA's Sixth Man of the Year, with about seven minutes left in the game when Smith swung his elbows, catching Terry in the face. Terry got up and was restrained by teammates, coach Doc Rivers and referee Dan Crawford.
The officials called a foul and after a video review ruled it a Flagrant 2, meaning an automatic ejection.
Smith finished the game with 15 points, four rebounds and three assists.