Hamilton had a leadoff double in the fourth inning Wednesday night, and was safe at second with a headfirst dive. He then scored on a single by Nelson Cruz.
But when the Rangers took the field in the top of the fifth, Marlon Byrd replaced Hamilton in center.
The Rangers said Hamilton would be evaluated Thursday and that he was day to day.
Texas was playing its first game since finding out that All-Star third baseman Michael Young will miss at least two weeks because of a strained left hamstring.
Hamilton was on the disabled list twice earlier this season, both times after crashing into outfield walls making catches. He strained a rib cage muscle the first time, then needed surgery the second time to repair a slight abdominal tear.
Before hitting two homers in the second game of a doubleheader Tuesday, Hamilton had gone 23 games and 99 at-bats since going deep.