Post spokesman Bob Jenkins says the soldier died at approximately 10:20 a.m. Tuesday at Blanchfield Army Community Hospital.
No one else was injured.
Lt. Col. Brian DeSantis, public affairs officer for the 101st Airborne Division, said initial indications are that the shooting was accidental. Jenkins said the post is withholding the soldier's name until the family has been notified.
The incident is still under investigation.