The shooting happened early Saturday morning on the fifth floor of St. Vincent's Hospital.
Police Sgt. Johnny Williams said that police received a call about an armed man walking in the hospital. When two officers confronted the man, the suspect opened fire, wounding one of the officers. The second officer shot back, mortally wounding the suspect.
Two employees were injured by gunfire. The injuries suffered by the police officer and employees were not considered life-threatening.
William said detectives were still trying to determine Saturday why the armed man was in the hospital.