A car and a van were in collision on Burren Road, near Warrenpoint, at about 14:20 GMT on Friday.
Insp Stephen Graham said a passenger in the car "is reported to have been seen making off from the scene across nearby fields whilst the driver of the car remained trapped in the vehicle".
The police helicopter took the 18-year-old man to hospital in Belfast.
The driver of the van was treated in a local hospital for non-life threatening injuries.
A police patrol car came upon the scene of the collision, and the office of the Police Ombudsman has been informed about the incident.
Police have appealed for information about a road crash in County Down that left a teenager critically injured.