Sizemore, 27, suffered the injury during the A's first full-squad workout on Saturday.
In 110 games last year with Oakland and Detroit, the Virginia Beach native batted .245 with 11 home runs and 56 runs batted in. He was traded to the Athletics by the Tigers on May 27 for pitcher David Purcey.
Sizemore underwent an MRI on Monday, and will be reexamined in two weeks to determine a date for surgery.
In two major league seasons, the former fifth-round pick has compiled a .239 batting average with 14 homers and 70 RBI.