Joe Garagiola, Jr., senior vice president of standards and on-field operations for Major League Baseball, made the announcement on Saturday.
Clevenger did not appeal the decision, and served the suspension Saturday, missing the Cubs' game against the Pirates.
"Whatever happens there, that's the decision of Major League Baseball," Cubs manager Dale Sveum said. "We're lucky it's just one day."
Cubs pitcher Manuel Corpas and bench coach Jamie Quirk also were ejected from the game, but neither was suspended.
Sveum gave Clevenger the news on Saturday.
"I fully accept it," Clevenger said. "Major League Baseball stepped in, and I accept their punishment."
It wasn't clear exactly what Clevenger did, and he didn't expand.
"When benches clear, things happen," he said. "I'm out there trying to protect my team. We'll go from there."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.