Kelly, ranked No. 4 among the Padres' top prospects, had the procedure performed by noted orthopedist James Andrews in Pensacola. Kelly then returned to his Florida home to relax before heading to San Diego.
"They went in and said it was a significant tear," Kelly said. "But they said the surgery went well."
Kelly won't be able to do a lot initially but has removed the brace on occasion to do some range-of-motion exercises with the training staff.
"Everything is going slow," Kelly said. "We're letting it heal. In about 12 to 14 days, they'll remove the stitches."
For now, Kelly is adjusting to working with one good arm -- his left arm, no less. It's been an adjustment so far.
"There's a lot of things you don't think of … like brushing my teeth, eating, opening doors," Kelly said.
Kelly has already tapped into two players who had similar surgery a year ago, pitchers Cory Luebke and Joe Wieland, for advice.
"Having those guys around helps if I have questions," he said.
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.