Hamilton, who is hitting .287 with 42 home runs and 123 RBIs, did not take the field in the fourth inning and was replaced by Leonys Martin during the Rangers' 11-3 loss to the Angels.
Rangers manager Ron Washington did not know how long Hamilton would be out of the lineup.
"We'll wait and see how he is Wednesday," Washington said. "He told me he was having vision troubles, a sinus infection."
Hamilton left the ballpark by the time reporters were let into the clubhouse after the game.
The Rangers' lead remains three games over Oakland in the AL West, while the Angels pulled within 6½. Los Angeles is three games out of the final AL wild-card spot.