The league also publicly reprimanded McCaffery for violating the Big Ten's sportsmanship policy and fined the school $10,000. Neither the suspension nor the fine can be appealed.
McCaffery will miss Thursday's game against Northwestern. Assistant Kirk Speraw will coach the Hawkeyes in his place.
"I think it's important to point out that my passion and energy come from a good place," McCaffery said Tuesday during a news conference in Iowa City. "I want my players to play that way. We ask them to play that way, and I'm going to fight for my guys. That's what I'm going to do. That will not stop. But I think in that instance, without question, I lost my cool, and you can't do that.
"I'm not perfect. Nobody is. I'm not going to beat myself up over it. I'm not happy about it. I'm not proud of it. We're all, every one of us is never too old to learn, especially from your mistakes."
Upset about a couple of calls made by the officiating crew, McCaffery picked up two technical fouls and was tossed from the game with about 12 minutes to play in Iowa's 75-71 loss to the No. 4 Badgers.
"We accept the ruling of the Big Ten Conference and as a result Fran will not coach his team Thursday evening," Iowa athletic director Gary Barta said in a statement. "We all look forward to putting the incident behind us. ... Fran continues to have my full support moving forward."
The Associated Press contributed to this report.