Conference USA commissioner Britton Banowsky announced the penalty, saying that "instances of flagrant misconduct require suspension."
Coleman, the team's second-leading scorer at 18.1 points per game, was ejected from the contest with 9:51 left in the second half. Arizona rallied for a 96-90 win in overtime.
Coleman expressed regret on Sunday.
"I want to apologize to Chase Budinger for what happened Saturday night. I never meant to step on him," Coleman said in a statement issued by the school. "I have never been in an incident like this before, and I have nothing but respect for him as a great player.
"I love the game too much to do something like that intentionally. I want to say I am sorry from the bottom of my heart," Coleman said. "I know that God knows what is in my heart, but I am hopeful that Chase will understand and forgive."
Coleman will serve his suspension on Wednesday when Houston plays UTEP.
"The University of Houston has always and will continue to uphold the highest levels of sportsmanship in every respect," Houston athletic director Dave Maggard said in a news release. "We apologize to the University of Arizona, its basketball team and to the Tucson community for what occurred Saturday evening. Aubrey will be suspended for Wednesday night's game, and we now consider the matter to be closed."
Information from The Associated Press was used in this report.