Hamilton, who leads the American League with a .361 batting average and has 31 homers with 97 RBI, has been bothered by pain since he crashed into the wall at Target Field in Minneapolis Sept. 4 while making a catch.
Previous X-rays and an MRI didn't turn up the broken bones, but a third exam by a California back specialist did, MLB.com reported.
"It's almost a relief to know there was such pain for a reason," Hamilton told reporters in Anaheim, Calif., where the Rangers were playing the Los Angeles Angels.
He added he's hopeful of playing again in the regular season before Texas makes a likely playoff appearance. The team's magic number to clinch the American League West crown was six entering Tuesday's game.
Hamilton told MLB.com he received injections to reduce the inflammation and block the pain and expects to resume his workouts within a few days.