Major League Baseball officials said Thursday that Cueto took "violent and aggressive actions" during the fight. The suspension would begin Friday unless he appeals.
The argument began Tuesday when Cincinnati's Brandon Phillips and St. Louis catcher Yadier Molina exchanged words. Phillips had previously made inflammatory comments about the Cardinals and also tapped Molina's shin guards with his bat.
Both benches quickly emptied. In the melee Cueto, the starting pitcher for the game, was pinned against the screen behind home plate and tried to kick his way loose.
In addition to the suspensions, MLB fined Cueto, Baker, La Russa, Phillips, Molina, St. Louis pitcher Chris Carpenter and Cincinnati pitcher Russ Springer were fined undisclosed amounts.