The right-hander was originally expected back in the A's rotation by the end of the month after undergoing his second Tommy John surgery last spring.
"You cross your fingers obviously for Jarrod," said A's manager Bob Melvin. "I don't even know what to say. For a guy who's worked as hard as he has to get back, I really don't have words for that, I just feel really bad for him. We have our fingers crossed it's not too bad."
Griffin shut down his rehab Thursday to attend to shoulder soreness, throwing just two innings of a scheduled three-inning simulated game before he had to stop.
"We're hoping it's just some inflammation," said Melvin.
• Closer Sean Doolittle (shoulder) faced live hitters for the first time Friday, totaling 15 pitches pain-free to teammates Max Muncy and Josh Phegley.
• Ben Zobrist (left knee surgery) is expected to begin taking batting practice when the club returns home next week.
• The A's traded relief pitcher Chad Smith to the Angels in exchange for cash Friday, one day after the club designated the right-hander for assignment.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.