Ibaka and Johnson were ejected after trading punches at 7:50 of the third quarter. The skirmish began when the two started shoving each other while waiting for the ball to be inbounded under the Miami basket. Officials reviewed the incident before giving both players technical fouls and ejections.
Johnson apologized on Twitter.
Tempers flared again after the final whistle, with DeRozan appearing to yell at Dragic as the teams left the court.
Ibaka ($138,357) and Johnson ($96,172) will lose close to $250,000 in salary based on the one-game suspensions. Toronto will get a $69,179 credit toward the luxury tax and is now $1.09 million below.
ESPN's Bobby Marks and The Associated Press contributed to this report.