Hamilton was acquired from the Angels on April 27 and wasn't activated by the Rangers until May 25 after 12 games on medical rehabilitation assignment.
"He has had a history of some injuries," Rangers manager Jeff Banister said. "The lack of Spring Training, we have talked about it already, it's the nature of where we are right now. We are trying to get his lower half right, keep it strong and keep it playable."
Hamilton has played in just 10 games for the Rangers, hitting .303 (10-for-33) with two home runs and five RBIs.
"We're going to give it every single effort to get it right," Banister said.
With Hamilton out, the Rangers used Delino DeShields in center field and Adam Rosales in left on Sunday. DeShields was also batting in the leadoff spot in his first game after being activated off the disabled list.
The Rangers also had Ryan Rua in right field so that Shin-Soo Choo could get a day off with left-hander C.J. Wilson on the mound for the Angels. Banister said the Rangers wanted to use Monday's off-day to give Choo two days in a row.
"[Choo's day off] does fall with the left-hander on the mound, but that wasn't the deciding factor," Banister said.
• Right-handed pitcher Dillon Tate, the Rangers' top pick in the June Draft, was scratched from a start at Class A Spokane on Saturday with triceps tendinitis.
• The Rangers have signed international free-agent shortstop Cristian Inoa from the Dominican Republic. He is described as an aggressive right-handed-hitting middle infielder who stands out for his game-playing ability and bat control. He played in La Javilla, a Santo Domingo youth league where Rangers Minor League outfielder Nomar Mazara also starred.
• The Rangers, going into Sunday, average 5.43 runs per game when DeShields hit leadoff, and 3.84 in all other games.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.