Left-hander Braden, who was placed on the 15-day disabled list on April 17, will undergo surgery in New York on Monday to repair a torn capsule in his left shoulder.
"Recovery time will be determined following the procedure," the team said in a statement.
Braden, 27, has posted a 1-1 record with a 3.00 ERA in three starts this season, yielding 18 hits with 15 strikeouts and five walks in 18 innings.
He is best known for his flawless performance against the Tampa Bay Rays on Mother's Day last year when he tossed the 19th perfect game in MLB history.
In front of a stunned crowd that included his grandmother, Braden retired all 27 Tampa Bay batters in a 4-0 victory.
His effort also handed Oakland their first perfect game since Catfish Hunter's 4-0 mastery of Minnesota in 1968.
(Writing by Mark Lamport-Stokes; Editing by Frank Pingue)