Cincinnati Reds Manager Dusty Baker was suspended for two games, and New York Yankees Manager Joe Girardi and San Diego Padres hitting coach Wally Joyner were penalized one game each Friday after recent arguments with umpires.
Major League Baseball also fined all three undisclosed amounts.
Girardi was suspended for kicking dirt that landed on plate umpire Chris Guccione in the ninth inning of Thursday night's 2-1 win over the Baltimore Orioles.
Girardi disputed a foul tip that became strike three on Jason Giambi and drew his first ejection as Yankees manager.
Baker made contact with umpire Eric Cooper during a dispute in the seventh inning of Thursday night's 8-2 loss at San Diego. Baker went on the field after Cincinnati's Edwin Encarnacion was ejected by Cooper.
Joyner was penalized for going onto the field to argue Wednesday against the St. Louis Cardinals.
Cox, 67, is the winningest manager in franchise history. He is in his 27th season as a manager, including 23 years with the Braves, and has said in recent years he had started to think about retirement.