Stauffer had been expected to start Thursday's season-opener against the Los Angeles Dodgers, but manager Bud Black said on Sunday that he was bothered by soreness in his arm.
To take Stauffer's roster spot, the Padres recalled right-hander Brad Brach from Triple-A Tucson. Brach is making his first appearance on an opening day roster after posting a 3-1 record and 1.69 ERA in 12 relief outings during spring training. He made his big league debut with the Padres last season, going 0-2 with a 5.14 ERA in nine relief appearances.
Right-hander Erik Hamren cleared outright waivers and has been assigned to Double-A San Antonio.