Terry was guarding Smith with about 7 minutes left in the game when Smith swung his elbows widely, catching Terry in the face. Terry popped up and had to be restrained by teammates, coach Doc Rivers and referee Dan Crawford.
The officials immediately called a foul, and after video review ruled it a Flagrant 2, meaning an automatic ejection.
The Knicks entered the game with a 2-0 lead in the best-of-seven series.
Smith, the NBA's Sixth Man of the Year, finished with 15 points, four rebounds and three assists.