Billingsley has twice had his rehab from last year's Tommy John surgery shut down because of discomfort, and he underwent a contrast MRI that revealed the flexor tendon damage. The repaired ulnar collateral ligament is intact.
Billingsley, 29, is receiving $12 million in the final guaranteed year of a three-year, $35 million contract that includes a $3 million buyout or a $14 million salary for 2015.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.