Anderson is 1-1 with a 2.35 ERA in four starts this season. He agreed to $12.5 million, four-year contract on April 16 that includes team options for 2014 and 2015. The total value of the deal could reach $31 million.
Oakland manager Bob Geren says Anderson was scheduled to undergo a contrast MRI on Tuesday. His replacement in the rotation has not been determined.
Tolleson is the son of former major leaguer Wayne Tolleson.