Rangers executive vice president/communications John Blake said the spectator was "able to move all his extremities and was responsive to paramedics."
Texas' Nelson Cruz fouled a ball into the first row of seats in the club level along the first-base line, and the fan attempted to snag the ball before losing his balance and tumbling about 30 feet onto the seats below.
Paramedics were on the scene quickly to attend to the fan, who was strapped to a stretcher and taken by ambulance to John Peter Smith Hospital.
The game was stopped for 16 minutes and several players on the field looked shaken.
Four people in the lower deck were struck when the spectator fell and were treated at the ballpark for minor injuries.