"We're excited to have Quack in our 'pen," said Padres manager Bud Black. "He pitched well for us last year and pitched well in El Paso."
Quackenbush, a right-hander, had a 1.50 ERA in six innings with nine strikeouts and two saves in two opportunities at El Paso.
He pitched well in Spring Training, but because the Padres added depth in the offseason, and Kelley was one of those acquisitions, Quackenbuch began the season in Triple-A.
"It's always tough to hear you're going back down to Triple-A," Quackenbush said. "But I'm happy to be back. The team is playing great, and I'm happy to be a part of it."
Quackenbush had a 2.48 ERA and six saves in 56 appearances (54 1/3 innings) with the Padres last year.
Kelley has struggled in a small sample size of outings this season, allowing six earned runs on nine hits and five walks over 5 1/3 innings.
"I felt it cramp up in the game the other night and didn't think it was a big deal, but then it got a little tighter overnight and the next day," Kelley said. "I don't think it's going to take too long or it's too serious, but the nature of our game, they need us out there every night."
Kelley has been watching video from last season when he was with the Yankees and compared it to video of his struggles with the Padres. He noticed a few mechanical fixes that he's working on, including keeping his front shoulder closed during his delivery.
Kelley said his time on the DL will allow him to continue his video study and his conversations with pitching coach Darren Balsley about getting him right for when he returns.
"I'll continue what I've been working on and get my calf healed up. When that's good to go, I'll get in some games and get back," he said. "I'll take advantage of this time. I feel a lot better than where I was the first three outings. I'll continue to work at it."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.