Johnson and referee David Jones both tugged at the ball after a Portland free throw in the third quarter. After Jones ejected him and started to walk away, Johnson threw his mouthpiece in Jones' direction.
Teammates had to restrain Johnson before he was escorted from the floor.
Johnson will miss Toronto's home game against Brooklyn on Wednesday night.
Johnson said after Monday's game that he has a habit of rubbing the ball before handing it to the ref during free throws. Although it appeared that the two had words, Johnson claimed nothing much was said.
He said he got frustrated when he wasn't given an explanation for the ejection.
"I guess the ref didn't let me have the ball, so we kind of got into a tug-of-war," Johnson said. "No words were really said, and he rejected me out of the game, and I kind of lost my cool from there."
Johnson, a reserve forward/center, is averaging 7.3 points and 5.4 rebounds this season. He finished the game with four points and four rebounds in a little more than 10 minutes.
Raptors coach Dwane Casey said the reaction was uncharacteristic for Johnson.
"I don't know what happened with Amir. He kind of lost his mind there for a little bit," Casey said Monday. "I told him we can't have that on a night where we're short-handed and we're in a situation where we're scrambling. We just gotta have more discipline than that."
Johnson agreed that it was unusual for him to act out.
"My teammates know me, my parents know me. ... I never lose my cool. I never said anything to a ref or got mad," he said Monday. "The only techs I've gotten were for hanging on the rim or slapping the backboard."
Johnson, who is in his eighth NBA season, was contrite after the game.
"I think it was just really childish. It was something that didn't need to happen," Johnson said. "I lost my cool, and I apologize on my part."
Information from The Associated Press was used in this report.