https://www.quora.com/Why-are-baseball-players-not-arrested-for-assault-when-they-charge-the-mound-and-start-a-fistfight-Anywhere-else-outside-of-the-game-they-would-be
Law enforcement generally allows the league to handle these events. Most would be classified as misdemeanor battery so punishments imposed by the league are greater than those a court could assess.
When players are suspended by a team or MLB they forfeit pay. A major league player on minimum wage loses more than $3000 for every game he’s ineligible to play. Jose Bautista’s one game suspension for the infamous fight with Roughned Odor cost him over $86,000