Kelly was placed on the 7-day injured list at Triple-A Worcester with a right elbow injury, Chris Cotillo of MassLive.com reports.
Kelly has made 17 appearances out of the Red Sox's bullpen this season, holding a 3.31 ERA and 14:7 K:BB over 16.1 innings. It's unclear how long he might be out, but Kelly won't be an option for the Red Sox in the immediate future.