Kelly has a blood clot in his right calf and is without an official timeline, Theo Mackie of The Arizona Republic reports.
Manager Torey Lovullo compared Kelly's situation to that of Ian Kennedy, who missed 18 days last year with a blood clot, though he wouldn't give any sort of timeline for Kelly. The right-hander was placed on the 15-day injured list Tuesday and will have an opportunity to get some added rest prior to a potential return after the All-Star break.