Byrdak, 34, was 3-0 with 3.20 ERA in 45 innings for the Tigers last season.
He will report to the Triple-A Round Rock Express in Iowa.
Byrdak struck out 9.8 batters per nine innings, ninth-best among all American League relievers last season. He limited left-handed batters to a .176 batting average (12-for-88) with the Tigers. Righties hit .268 (26-for-97) with Byrdak on the mound.
He went on the disabled list on June 27 with left elbow tendinitis and rejoined the Tigers on July 25.
Byrdak began the 2006 season with the Balitmore Orioles and was on the Opening Day roster at the Major League level for the first time.
Sandy Burgin is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.Less