The decision was made after Hamilton reported increased discomfort following the team's 2½-hour flight to Detroit on Wednesday evening, according to the Dallas Morning News.
Hamilton's sore knee forced him to miss the Rangers' previous four games. He will be eligible to return on Aug. 31.
Hamilton underwent an MRI last week after the lingering soreness in his knee sidelined him for two games. The test revealed no structural damage.
"Just getting old. Thin cartilage. Same thing as I figured it was, like a bone bruise," Hamilton, 34, said at the time. "Mentally, I know it's structurally fine, so the pain part of it is fine."
Hamilton has not ruled out offseason surgery to potentially repair or remove some cartilage in his knee. A five-time All-Star and the 2010 American League MVP, he has already undergone knee surgery twice on each knee.
Since being reacquired by the Rangers this year from the Los Angeles Angels, Hamilton is batting .254 in 142 at-bats with a career-low .726 on-base-plus-slugging percentage.
The Rangers (61-59) currently trail the Houston Astros by four games in the American League West.
The Associated Press contributed to this report.