Kelly was held out of workouts on Sunday after he reported the strain. It wasn't one specific incident that led to it, he said.
"It was kind of a gradual thing," Kelly said. "It just got tighter and tighter. Right now, we're just getting treatment on it."
There's no timetable to when Kelly will be able to resume workouts, including throwing off the mound.
Kelly, who had Tommy John surgery in 2013 and was limited to 20 1/3 innings last season in the Minor Leagues when his rehabilitation hit a snag, threw a bullpen session on Friday and came out of that fine, he said on Saturday.
Kelly is expected to get stretched out as a starting pitcher in camp and then begin the season with one of the team's Minor League affiliates, starting every fifth day.
"This is going to be a slow process with Casey, but the key thing with him is that when he did throw his side [Friday], he felt great," said Padres manager Bud Black.
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.