Parker, who is attempting a comeback from a second Tommy John surgery, suffered the latest injury on May 8 while pitching on a rehab assignment with Triple-A Nashville.
The surgery will be performed in Florida by Dr. James Andrews. The Athletics have not disclosed a timetable for when they expect Parker to pitch again.
Athletics manager Bob Melvin said, however, that Parker likely will not need another Tommy John surgery on his ulnar collateral ligament.
"My understanding is that the ligament is intact and it is just the bone they're working on," Melvin told reporters Monday, according to the San Francisco Chronicle. "But you never really know until you get in there."
Parker took to Twitter on Tuesday morning, expressing optimism over his future.
The Associated Press contributed to this report.