Stauffer, who went on the disabled list on April 4 with a strained right elbow, threw 78 pitches in his rehabilitation start on Wednesday for Class A Lake Elsinore and then threw a side session before the start of Friday's game against the Phillies.
"He pitched so well for us last year and it looked throughout the winter that he was on a nice path to a good year," Padres manager Bud Black said. "It was a detour for Tim. He feels good, his pitch count is where it needs to be and physically and mentally he feels where he needs to be."
Stauffer first experienced discomfort in his elbow late in Spring Training. Edinson Volquez was named the Opening Day starter.
While Stauffer will start Monday, Black indicated that Anthony Bass will start Tuesday. He'll be followed by Clayton Richard on Wednesday when the team returns home to Petco Park to face the Dodgers.