Castellanos has also been handed an undisclosed fine.
He is appealing the suspension, which MLB's senior vice president for on-field operations Michael Hill said was given for "aggressive actions and for instigating a benches-clearing incident."
On Saturday, Castellanos was ejected from the game for his role in the confrontation, which ensued after bumping into pitcher Jake Woodford as he slid into home plate on a wild pitch. Upon standing up, Castellanos yelled and flexed in front of the pitcher.
"I'm not out here to disrespect nobody or whatever, but I want to win,'' Castellanos said after Saturday's 9-6 win.
"There is no need to stand over somebody and taunt somebody," St. Louis manager Mike Shildt said Saturday.
Cardinals third baseman Nolan Arenado, pitcher Jordan Hicks and catcher Yadier Molina, and Reds infielder Eugenio Suárez and outfielder Jesse Winker have also been fined for their roles in the incident.
The Reds (2-1) host the Pirates on Monday night in the first game of a three-game series.