Reliever Cory Burns was recalled from Triple-A Round Rock to replace Ogando, and Josh Lindblom is expected to start against Oakland on Monday.
Washington suggested Ogando's problem is minor and it might have something to do with his increased workload as a starter. He was used as a reliever in 2012 before being moved to the bullpen this season.
"He's a starting pitcher and he's taken on a big work load," Washington said. "Rather than letting this drag on, we're going to nip it in the bud and get it right. Otherwise, he'll take the ball and go back out there."
Ogando is scheduled to have an MRI at some point and will be eligible to come off the disabled list on May 31. The Rangers now have three veteran starters on the disabled list. Matt Harrison is still recovering from back surgery and is likely to be out until August.
Colby Lewis, who had flexor tendon surgery 10 months ago, is getting closer to returning. He had a minor bout of triceps tendinitis earlier this week and was recalled from his medical rehabilitation assignment, but he is scheduled to throw a bullpen session on Friday and start on Monday for Double-A Frisco.
Despite the injuries, the Rangers went into Thursday with a seven-game lead in the American League West.
"It just means we have pretty good depth," Washington said. "Drama ... adversity ... those guys in the clubhouse are used to it. Somebody has to step up. If you don't step up, somebody else will step up."
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.