Hill exited early from his most recent outing on May 29 against the Tigers, and he has not pitched in a game since then. The 36-year-old was scheduled to throw 35 pitches on the side at Miller Park on Wednesday, but he aggravated his groin in doing so.
Hill said he felt a "grabbing, pulling sensation" on his 33rd and 34th pitches, "essentially what I felt in the seventh inning [vs. Detroit]."
That led the A's to schedule Hill for an MRI on Thursday, and they subsequently placed him on the DL.
Hill is 8-3 with a 2.25 ERA in 11 starts this season, and he was named the American League Pitcher of the Month for May.
David Adler is a reporter for MLB.com based in New York. Follow him on Twitter at @_dadler. This story was not subject to the approval of Major League Baseball or its clubs.