MLB senior vice president for on-field operations Michael Hill announced the suspension Tuesday in response to Garrett's actions Saturday in Cincinnati.
Garrett entered in the top of the eighth inning of the Reds' 3-2 loss to the Cubs on Saturday at Great American Ball Park. He struck out Cubs first baseman Anthony Rizzo in his first exchange.
Garrett celebrated the strikeout with screams and gestures toward the Cubs dugout.
The Cubs and Reds reacted by running out of their respecting dugouts. Players met near the third base line for a brief skirmish. They then returned to their respective dugouts. Garrett forced a fly out in the next at-bat. No players were ejected for the on-field delay.
Garrett's suspension was scheduled to start Tuesday, but he appealed the disciplinary measure and can play until MLB rules on the appeal.
MLB fined Cubs infielder Javier Baez an undisclosed amount for his role in the incident.
The Reds won two of three games in the series against the Cubs. They host the Chicago White Sox at 12:35 p.m. EDT Wednesday in Cincinnati. The Cubs host the Los Angeles Dodgers at 7:40 p.m. EDT Wednesday at Wrigley Field in Chicago.