Sheets was examined by Texas Rangers team physician Dr. Keith Meister on Wednesday, who said Sheets has a tear and would not pitch again this season.
A's manager Bob Geren said no surgery is currently planned, although Sheets needed an operation to repair the same injury when he missed the 2009 season for the Milwaukee Brewers.
Sheets was placed on the 15-day disabled list last Saturday.
The A's signed the 32-year-old former All-Star to a one-year, $10 million free-agent deal in January. He finished the season 4-9 with a 4.53 ERA in 20 starts.