The Rangers have no current plans to put Hamilton on the disabled list, but Hamilton will undergo an MRI exam administered by Dr. John Preskitt on Monday.
Hamilton sustained the injury on May 17 in a home game against the Los Angeles Angels when he crashed into the padded outfield wall while making a leaping catch.
The injury was described at the time as a slight groin pull and the 2008 All-Star has remained in the lineup. But he was in a 3-for-23 slide during the seven-game homestand that concluded Sunday.
"It's a great idea," Hamilton said of taking the day off. "If I can't run, I can't play. We'll see what the doctor says."
Hamilton singled in the ninth as a pinch hitter.
Manager Ron Washington said Hamilton has been limited, but he thinks his condition could show improvement by missing Sunday's start and with Monday's off day.
"When you're battling injuries, sometimes you can't drive [the ball] the way you want to drive it," Washington said.
Marlon Byrd started in center field in place of Hamilton, who had a breakout season in 2008 with a .304 average, 32 homers and 130 RBIs.
This season Hamilton is hitting .240 with six homers and 24 RBIs.
Earlier this season Hamilton missed 13 games with a rib injury sustained when he crashed into the outfield wall in Toronto.