It appeared from television replays that Murphy, who was out, ran his knee hard into Rodriguez's shin guard during the collision.
Murphy was on the ground for a few moments, too, and left in the fourth inning after returning to left field to start the third.
Murphy returned to left field in the top of the third but left the game in the fourth. The Rangers said Murphy had a strained ligament in his right knee and would have an MRI on Thursday.
Jose Molina came in to bat for Rodriguez in the third. He singled and later scored in a three-run inning for the Yankees. Brandon Boggs replaced Murphy.
The Yankees acquired Rodriguez from Detroit last week on the same day as catcher Jorge Posada's season-ending shoulder surgery.
