The southpaw began the year in Texas' rotation, going 0-5 with a 6.95 ERA in seven starts before he went on the DL on May 17 with inflammation in his left shoulder.
Hamilton appeared in seven games for the Rangers after returning from the DL on May 25, batting .273 with two home runs and five RBIs. He's expected to miss about four weeks.
"It's just like I've always dealt with anything else," Hamilton said of the setback. "Whatever the situation is, you pick yourself up and you go forward, not looking back at what happened but what's in front of you, make things right, get better and just continue to do the same things that I did when I was trying to come back this last time and let pain be my guide. I've traditionally healed pretty fast from things."
Hamilton worked quickly to get back to the Majors after undergoing shoulder surgery in February and did not participate in Spring Training before the Angels traded him in late April. He went to extended spring training for a couple of weeks, then played in 12 Minor League games on a rehab assignment before returning to the Rangers.
"I played a lot of games pretty fast to get back to this point," he said. "I have no regrets as far as the way I went about getting back."
In additional moves, infielder Thomas Field was outrighted to Triple-A Round Rock after he was designated for assignment on Saturday, and outfielder Ryan Rua was sent to Round Rock to begin an injury rehabilitation assignment (right heel fracture).
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.