A spokesman for the American League-leading Rangers told Reuters that Hamilton, who missed the last two games with vision problems, was back in Texas to be further examined but offered no timetable for the five-time All-Star's return.
Hamilton left Tuesday's game against the Los Angeles Angels after two at-bats and has not played since. He said the problem was sinus related.
"Every time I get sick it turns into a sinus infection, and that causes me to get off kilter, off balance. If your head's a little stopped up, you can get a little starry-eyed, dizzy."
Hamilton said he had his vision checked and it was good.
"It's 20/15," said the 31-year-old. "It used to be 20/10 but I'm getting older."
He leads MLB with 42 home runs and is batting .287 but has missed 11 games this season with various problems.
Rangers manager Ron Washington ruled Hamilton out of Thursday's game with the Angels after the 2010 American League most valuable player took batting practice.
"If I feel I can play, I'll play," Hamilton said. "I've played through sinus stuff before. This time of the season, it matters tremendously. ... I don't want to misjudge a ball out there. These are too big of games."
The Rangers lead the American League West division by four games over the Oakland Athletics with a 89-60 record and 13 games remaining.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Frank Pingue)