Griffin will likely play catch for a week or so before graduating to the mound. His return is expected to be around the All-Star break.
"When I get hurt, I turn off my brain, listen to my body and do what the trainers tell me to do," Griffin said. "Try not to get ahead of myself."
Griffin is 4-2 with a 5.77 ERA in eight starts. He won four straight starts from April 12 to May 9, but is 0-2 with a 15.83 ERA in his past three.
Rangers ponder Ross situation Rangers pitcher Tyson Ross did not have the kind of outing on Friday night that would lend credence to the idea he is ready to return to the Major Leagues.
Ross allowed eight runs on 10 hits over five innings for Triple-A Round Rock at Oklahoma City. It was his fourth rehab outing as he tries to complete his recovery from offseason shoulder surgery.
Ross is expected to join the team in Houston on Monday, and they will discuss his next assignment, whether he pitches for the Rangers or another start for Round Rock. His 30-day rehab assignment expires June 21, so he has time for two more Minor League starts.
"The No. 1 factor in the decision-making process is to be healthy," manager Jeff Banister said. "All indications are he is healthy."
Rangers beat • Pitcher Cole Hamels, on the disabled list with a strained right oblique muscle, threw a bullpen session on Saturday. If he recovers from that without issue, the next step would be live batting practice.
• Rangers third baseman Adrian Beltre is one of eight players in Major League history who has hit a home run in 40 different parks. But he has never hit a home run in Washington, at either RFK Stadium or Nationals Park.
• Outfielder Carlos Gomez, on the disabled list with a strained right hamstring, began a medical rehabilitation assignment for Triple-A Round Rock on Saturday.