Chriss has been suspended one game by the league.
Both bans are without pay. Ibaka will lose $448,276 in total salary; Chriss will forfeit $22,111.
Ibaka went to the floor after the two were battling for position under Cleveland's basket as the Raptors attempted a full-court pass that sailed out of bounds.
Ibaka shoved Chriss from behind and grabbed near his neck before throwing a punch. Chriss responded with a punch before players from both teams separated the two. Ibaka immediately headed for the locker room, and both players were kicked out after the officials conferred.
In announcing the suspension, the league said that Ibaka's discipline was "based on his instigation of the physical altercation, throwing a punch at Chriss, and his prior history of fighting during NBA games" and that Chriss' punishment "was based on throwing a punch at Ibaka."
Cleveland was ahead 91-77 at the time of the incident and went on to win 126-101.
Earlier in the game, Ibaka hit the court hard in the second quarter after being fouled by Chriss after a rebound.
Monday's game marked the eighth ejection of Ibaka's 10-year career and the third for Chriss in three seasons.
Information from ESPN's Bobby Marks and The Associated Press was used in this report.