The team optioned outfielder Cedric Hunter to Triple-A Tucson and also reassigned left-handed pitchers Colt Hynes, Rob Musgrave and Kelly to Minor League camp.
Kelly did not allow a run in five innings in Cactus League games and allowed two hits. He did allow one run in three innings during a B game Monday against the Mariners.
"Very good, that's what we've seen the whole time ... a lot of composure," Padres manager Bud Black said on Monday. "He just needs to keep pitching. He's doing a lot of very good things."
Kelly was one of four players obtained from the Red Sox in the December deal that sent three-time All-Star first baseman Adrian Gonzalez to Boston.
Hunter opened eyes in camp, hitting .435 with four doubles, one triple, one home run and 10 RBIs.
Hynes, who worked a scoreless inning in Tuesday's 9-6 loss to the Angels, didn't allow a run in 5 1/3 innings.
Musgrave had a 3.60 ERA in four appearances spanning five innings.