A doctor said the man was still alive when he was taken to the emergency room but died soon after. He shot himself in the temple.
The Rockwood Cancer Treatment Center at the Deaconess Medical Center} was evacuated after the shooting on the seventh floor. Employees were allowed to return after police searched the building.
Police also shut down some roads around the hospital.
Later in the day, police said the building was open and patients being allowed in. The seventh floor remained closed as a crime scene.
Relatives and friends said the couple had two children. Police said the children were safe.