Bradley has been out of the lineup for seven straight games with a strained left quadriceps muscle but has appeared three times as a pinch-hitter.
Hamilton left Tuesday's game after four innings with inflammation in his left knee. Hamilton has been dealing with the problem for about a week, but during Tuesday's game he couldn't get good breaks on balls in center field or generate speed on the basepaths because of the pain.
"It's nothing big," Hamilton said. "I need a couple of days' rest, probably. I was thinking about playing today but I thought it might be better if I didn't."
Hamilton had surgery on his left knee in March 2006 and again that year in July.
"I'm sure if he was all we had, he'd go out there," Washington said. "But we have someone else so we'll put them out there. If it's bothering him then it is bothering us."
The Rangers should at least get one of them back on Friday when they return home to Arlington and are able to use the designated hitter again.
The Rangers did get Jamey Wright back on Wednesday as he rejoined the team after his wife delivered their second child on Monday.
He replaces Joaquin Benoit, who was unavailable on Wednesday after throwing 19 pitches in Tuesday's game. Benoit is still dealing with some soreness in his right shoulder but is trying to pitch through it.
T.R. Sullivan is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.