The fire service received a call at 7.55pm on Saturday, May 11 about the incident which occurred on Blue Bank on the A169 near Sleights.
Crews from Whitby and Lythe attended along with a volunteer crew from Goathland.
The drivers were out of the cars when crews arrived and were taken to hospital by the ambulance service.
The extent of their injuries is not know.
Both cars were completely burned out by the fire, the road remained closed for several hours while crews extinguished the vehicles.