The source told CNN the attacker fled the scene outside the Henry Dunant Hospital, in the 16th arrondissement of the French capital, using a two-wheeled vehicle. A motive is not yet known.
The geriatric hospital is run by the French Red Cross and it currently serves as a Covid-19 vaccination center.
Several gunshots were reported outside the hospital and the injured person was taken into care at the hospital.
This is a developing story.