Kimball, who made his major league debut on May 14, went on the disabled list on June 10 with right shoulder inflammation, and was shut down from a throwing program after he still had pain following rest and a cortisone shot. He'd pitched in 12 games for the Nationals, allowing just three runs in 14 innings, though he did let four of five inherited runners score.
"He just got here. He pitched well up here," manager Davey Johnson said. "It's an unfortunate injury. Hopefully he'll be alright and recover. That's part of the game, injuries, and we've had our fair share."
Kimball was not made available to reporters for comment.