The action came for their parts in an incident during a game against the New York Mets on April 6.
After both dugouts were warned by the umpires earlier in the game, Rodriguez hit Mets catcher Paul Lo Duca with a pitch in the eighth inning.
Emotions got the best of the Nationals after New York starter Pedro Martinez hit three batters, including outfielder Jose Guillen twice. Guillen took offense the second time he was hit and the right fielder had to be restrained by the home-plate umpire as the dugouts and bullpens emptied in the fifth inning.
Guillen, who was not suspended, was also fined an undisclosed amount, as were Robinson and Rodriguez.
The Nationals and Mets are scheduled to open a three-game series Tuesday in Washington, and both clubs have been instructed by Major League Baseball to keep things under control.
Celebrity Families of 2014 [PHOTOS]