Odor was injured scrambling back to first base on a pickoff throw by Indians catcher Yan Gomes on Sunday. The rookie never made it to the bag, stopping instead to grab his shoulder after planting his right hand in the dirt.
Cleveland first baseman Carlos Santana didn't try to tag Odor initially because he figured the throw was late. When Santana turned around and saw Odor hunched over on the ground, he tagged the runner out.
Odor will be re-evaluated Monday.
Mitch Moreland is about to become the 13th Texas player on the disabled list. He will be out three months for surgery on his left ankle.