Major League Baseball has fined, but not suspended, Cleveland Indians starting pitcher Trevor Bauer for Sunday's tantrum that resulted in him throwing the ball from the mound over the center-field fence, according to media reports Tuesday.

MLB Network was the first to report Bauer had been fined. The amount of the fine is not known.

Indians manager Terry Francona, meanwhile, hadn't decided what action, if any, the team will take regarding Bauer's outburst. He said he would discuss the incident further with team president Chris Antonetti and general manager Mike Chernoff after the trade deadline..

"'To be honest with you, I need to figure out what I consider is proper and respectful," Francona told reporters Tuesday. "I would never do something without Chris and Chernie's input. I thought they were so busy that it just wasn't right to put that on their plate.

"So there will be a time to get to that. After they hear from the league, and after they get a chance to settle down a little bit, we can discuss exactly what's right as we move forward."

Bauer threw the ball as Francona was coming onto the field to take him out of the game in the fifth inning of Sunday's 9-6 loss to the Royals.

After the game, Bauer apologized for his behavior.

"I want to be clear that my frustrations were with myself and my inability to stop the situation and keep my team in the game," Bauer said. "I'm an intense competitor. That fire is what drives me. Today, it completely consumed me and took over."

"... It was unbecoming. It was childish. Unprofessional. There's no place for it in the game."

The Associated Press contributed to this report.