The incident occurred early in the fourth quarter of the Rockets' 139-114 road loss Friday, beginning after Houston's Garrison Mathews fouled Sacramento's Malik Monk while they were pursuing a loose ball.
Mathews was fined $35,000 for initiating the altercation and taunting Monk. Houston forward Tari Eason was fined $30,000 for escalating the situation and making inadvertent contact with an official. Monk was fined $25,000 for continuing the altercation and taunting Mathews. All three players received technical fouls and were ejected.
Green and Tate served their suspensions during Sunday's road loss to the LA Clippers.
Houston has lost 15 of its past 16 games.