Posada came to bat in the second inning Sunday and fouled off the first pitch from Tampa Bay's James Shields, sending it into the seats along the first-base line, where it struck the woman.
Stadium medical staff attended to the woman, whose head was bleeding, and placed her in a wheelchair before she was removed from the stadium and taken to a hospital. The extent of her injuries was unknown.
On Friday, Rangers slugger Josh Hamilton fouled off a pitch in the sixth inning against Oakland and hit a fan in the face. That incident came one night after Hamilton tossed a ball into the seats and a fan fell out of the stands trying to catch it. The man died later that night.