Alvarez, who left his start for Nashville on Saturday in the fourth inning, is now expected to make a visit to Dr. James Andrews.
"I really do feel for him,'' A's manager Bob Melvin told reporters, according to the Bay Area News group. "He loves to pitch, loves to compete. He was looking forward to coming back and helping his team. It's pretty demoralizing, and I know he's having a tough time with it right now. He wants to contribute and pitch.''
The 26-year-old Alvarez underwent season-ending shoulder surgery last July and hasn't pitched in the major leagues this season. He signed a one-year contract with the A's in December after he wasn't offered a contract by the Marlins for the 2016 season.
A National League All-Star in 2014 when he was 12-7 with a career-best 2.65 ERA in 187 innings pitched for Miami, Alvarez went 0-4 with a 6.45 ERA in four starts for Miami last season, which was shortened by two stints on the disabled list for injuries to his right shoulder.
Information from The Associated Press contributed to this report.