Marlon Byrd filled in for Hamilton in center field, while David Murphy got his second straight start in left.
"It's just sore," Hamilton said Tuesday afternoon. "It feels better than yesterday, so that's a good sign. I'd like to play tomorrow, but we'll see."
Hamilton, who won the American League RBI crown last season, exited Sunday's home game against the Angles after crashing into the right-center-field wall to make a leaping catch. He reported a strained right groin muscle afterward, though he didn't call it a severe matter.
"The other day he could've went back out there," Rangers manager Ron Washington said, "but he came to me and he said, 'I would hate to go out there and have to extend myself when I just don't have it.'"
Hamilton returned from the 15-day DL last Tuesday. He suffered a strained rib cage muscle when he ran into the outfield wall in Toronto.
Washington said Hamilton's current condition isn't that serious.
"I think he could've played if we needed him today," Washington said. "But if he's close to being ready, we figured we'd give him another day."
The Texas skipper also saw a silver lining to Hamilton's absence. It gives Murphy a chance to gain experience.
Murphy is hitting .203 with one home run and eight RBIs this season.
"Every time I get a chance to get Murphy in there, I want Murphy in there," Washington said. "The possibility to get him some more at-bats, every time I get that chance I'm going to throw him out there, whether it's against a lefty or a righty."
Scott McNeish is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.