Police responded to a report of a road traffic collision on the B3236, Buckliegh Road, Westward Ho!, close to the entrance of Herons Lea residential care home, which involved a car and two horses just before 6pm, on Saturday 3 April.
Both horses were quickly gathered in but the riders suffered injuries that required hospital treatment.
The car involved was reported to have stopped at the scene for a short time but left before any details were exchanged.
It is thought the car, a white Dacia Sandero, was being driven by a man in his 70s, described as being of short, stocky build, with short dark hair.
Police are appealing for the driver to come forward, as well as any witnesses who may have information about what happened.
Anyone who has any information is asked to email [email protected] or call 101, quoting log number 811, of Saturday 3 April.
Source:: Devon and Cornwall Police News