The Rangers said Cabrera would serve the three-game suspension during their series against the Detroit Tigers, which begins Tuesday.
Cabrera tossed his gloves after his ejection in the sixth inning of a 4-2 victory over the Cleveland Indians on Thursday. Cabrera was upset about a called third strike by home plate umpire Doug Eddings.
After striking out for the third time in the game, Cabrera stayed momentarily at home plate and calmly expressed his displeasure with the call.
Cabrera saw video of the pitch after going back to the dugout, started chirping and was ejected by Eddings. Cabrera threw his gloves while crew chief Bill Miller was talking with Rangers manager Chris Woodward, and one of them hit Miller. Woodward said he also felt something hit his foot.
Cabrera's suspension came down Friday, in the same week that San Diego Padres third baseman Manny Machado was suspended for one game when Major League Baseball said he made contact with plate umpire Bill Welke after being ejected for arguing a called third strike.
The MLB Umpires Association strongly objected to the length of the Machado suspension and said so in a tweet, adding that, "Violence in the workplace is not tolerated,'' and asking, "Is this truly what MLB wants to teach our youth?'' MLB said it was inappropriate for the umpires' union to comment on the suspension.
On Friday, Woodward called Cabrera's suspension "pretty steep." The Rangers manager said he didn't see all of what happened with Machado in Colorado, and wasn't going to make comparisons to that incident.
"Anytime you make contact with an umpire ... even if it's like a feather, you're making contact, you've almost got to assume that there will be some sort of suspension,'' Woodward said. "I don't think [Cabrera] intended to hit the umpire. I think he was trying to show his disapproval.''