The left-handed Puk injured the ulnar collateral ligament in his left elbow, the team said Tuesday. Puk was initially diagnosed by Dr. Doug Freedberg in Arizona, and Andrews was consulted to confirm the 22-year-old's injury.
Puk was the sixth overall pick in the 2016 draft by Oakland out of the University of Florida. He struck out 184 batters in 125 innings split between Class A and Double-A last season, going 6-10 with a 4.03 ERA.
He pitched well this spring, holding opposing hitters to a .184 average in 10⅔ innings, and he was thought to have a chance to make the club.
But he did not pitch again after giving up four runs in his last outing on March 15 and feeling tenderness in his left arm.
"First and foremost, you feel sorry for him," A's manager Bob Melvin said. "He's a young guy. Typically when these things happen, these guys come back as strong if not stronger than ever. And I know he's going to work hard to get back and pitch in the fashion he was."
Another A's pitching prospect, Jharel Cotton, had Tommy John surgery last Wednesday.
"The hits just keep on coming as far as the rotation goes," Melvin said.
Information from The Associated Press was used in this report.