Hamilton had an MRI. Rangers assistant general manager Thad Levine says what had been a groin strain had migrated to the abdomen.
The injury is much like a sports hernia. Levine says a second opinion is needed before it is determined whether surgery is needed.
Levine says rest and anti-inflammatory medication might alleviate the injury.
Hamilton got hurt May 17 when he crashed into an outfield wall during a leaping catch against the Los Angeles Angels.
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Hamilton went on the DL retroactive to Monday.
Right-hander Vicente Padilla, sidelined since May 16 with a strained right shoulder, was activated and started tonight against the Yankees. To clear a roster spot for him, the Rangers optioned right-hander Guillermo Moscoso to Oklahoma City