Major League Baseball said Thursday that Cueto, Cardinals manager Tony La Russa and Reds manager Dusty Baker were also fined undisclosed amounts.
A fight broke out in the first inning of Tuesday's game in Cincinnati. The Cardinals won the game and swept a three-game series to move into first place in the NL Central.
"We regret the incident happened," Reds spokesman Rob Butcher said in a statement. "After a thorough investigation of the incident, MLB has handled the discipline accordingly for both clubs."
Cardinals spokeswoman Melody Yount said general manager John Mozeliak was traveling Thursday and unavailable for comment. She said he would be available to the media on Friday.
A statement from Major League Baseball that said all three suspensions are expected to begin Friday. Cueto could appeal, and the suspension would be delayed until the appeal is resolved. Managers can't appeal suspensions, Yount said.
The fight happened during a critical series made even more tense by comments from Phillips, who said that he hates the Cardinals. He also called them complainers, using demeaning language that riled St. Louis.
Phillips came to the plate in the bottom of the first inning and gave a friendly tap to Molina's shin guard. Molina kicked at the bat, mentioned Phillips' comments and told him not to touch him. The two went face to face, prompting both benches and bullpens to empty.
The scrum escalated into shoving that ended up with several players -- including Cueto and Carpenter -- pinned to the backstop screen. Cueto began kicking those around him -- he later said he was afraid and trying to defend himself. His spikes scraped Carpenter's back and La Russa said backup catcher Jason LaRue suffered a mild concussion and had sore ribs from the incident.
The Cardinals called up Double-A catcher Steven Hill for Wednesday's game because LaRue was unavailable.
The teams play one more series this season -- Sept. 3-5 in St. Louis.