Suppan was 2-3 with a 5.28 ERA since being recalled from Triple-A Tucson on May 2. He was out of the majors last season.
Suppan has pitched in the majors for 17 seasons. He has a career record of 140-146 with a 4.70 ERA.
The Padres recalled rookie catcher Yasmani Grandal from Tucson. He was one of four players San Diego received in an offseason trade with Cincinnati for right-handed pitcher Mat Latos. Grandal was hitting .317 with four home runs and 23 RBIs with Tucson.