The Rangers' cleanup hitter fell flat on his face behind first base after failing to beat out his inning-ending ground ball to shortstop. Byrd got up gingerly and walked toward center field, but nearly collapsed while the Rangers' training staff attempted to help.
Byrd, batting .281 with 20 homers and 89 RBIs, appeared frustrated as he limped back to the dugout. The Rangers later said Byrd had a right hip capsule strain.
Craig Gentry replaced him in center field for the bottom half of the first.
The Rangers were eliminated from the AL West race Monday, but still had a mathematical shot at the wild card. They trailed Boston by six games with six to play, but the Red Sox lost to Toronto earlier Tuesday.