McDowell is also accused of threatening a fan who objected to his actions with a baseball bat.
The former major league reliever apologized in a statement, but the team barred him from the bench heading into a three-game series against St. Louis.
"I am deeply sorry that I responded to the heckling fans in San Francisco on Saturday. I apologize to everyone for my actions," McDowell said in a statement.
The Braves' minor league pitching coordinator, Dave Wallace, will take over for McDowell during the investigation.
Major League Baseball said it's waiting to hear from the team before deciding on possible penalties.