Kelly said by text message that he hopes it's nothing more than inflammation.
San Diego manager Bud Black said that Kelly's soreness was located in the back of the elbow and not the ulnar collateral ligament, which was repaired April 2, 2013.
Kelly's recovery and rehabilitation to this point had gone by without much of a hiccup, and there was a good chance that he could have been pitching for a Minor League affiliate by the end of the month.
That could still occur if the soreness in the elbow subsides and he's able to resume his rehab protocol.
Last month, pitcher Joe Wieland, working his way back from Tommy John surgery in July 2012, had soreness in the back of his elbow, specifically the triceps. It was a recurring issue during his rehab. He eventually had minor elbow surgery to remove a piece of scar tissue that had caused him soreness.
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.