MLB.com reports that Parker "grasped his arm when throwing a wild pitch," and the San Francisco Chronicle reports that he experienced "excruciating pain" after throwing a pitch during his Triple A Nashville start.
The A's said they "will not have definitive details or a diagnosis until he sees a doctor."
Parker underwent his second career Tommy John surgery in March 2014 and missed all of last season. He had been expected to rejoin the team's rotation by the end of May.
The 26-year-old has not pitched in the majors since 2013, when he went 12-8 with a 3.97 ERA and threw 197 innings.
Oakland pitcher A.J. Griffin also experienced a rehab setback this week, the team said. He was shut down after two innings of a scheduled three-inning simulated game.
- Molly Geary