Clemens was suspended five games, Torre will have to miss one contest and both were fined an undisclosed amount.
Unless they appeal, their suspensions will begin Friday.
Both benches emptied after Towers hit Alex Rodriguez with a pitch in the third inning of what turned out to be a 9-2 New York victory Tuesday. No punches were thrown but warnings were issued to both teams.
Clemens then hit Alex Rios in the back during the seventh inning with New York in front, 7-0. Clemens and Torre were kicked out of the game.