"He's a big part of our team," manager Jeff Banister said. "We're going to miss him."
The Rangers will call up infielder Jurickson Profar, at least while Odor is suspended. Profar, who has missed the last two seasons because of a torn muscle in his right shoulder, has been playing second base recently at Triple-A Round Rock.
Odor was suspended for his role in an altercation with Blue Jays outfielder Jose Bautista in a game on May 15 in Arlington.