Peterson is on the 60-day injured list after having surgery to repair a torn labrum in his left hip, and he is likely to remain shut down for at least two months.
Hurt has been sent to the 60-day injured list with right shoulder inflammation, and he is not expected to be activated until at least the beginning of June.
Kershaw is expected to remain on the 60-day injured list until at least the end of July while he recovers from surgery to repair the gleno-humeral ligaments and capsule in his left shoulder.
May has been shuttled to the 60-day injured list after having surgery to repair his flexor and UCL in his right elbow, and he is not likely to suit up until the end of July.