Rob McGregor, 77, overtook a horse called Apollo near his home in a village near Selby and then drove off without stopping, York Magistrates' Court was told.
Although he was followed from the crime scene to his home, he initially denied any wrongdoing, and only changed his statement on the scheduled trial date.
Mr McGregor, of Westcroft Lane, Hambleton, pleaded guilty to careless driving and failing to stop after a collision.
He was given eight penalty points and ordered to pay more than £2,200 in fines, prosecution costs and a statutory surcharge.
York magistrates heard the horse's owner had to pay more than £470 in vet costs.
Speaking after the hearing, Detective Inspector Sam Potts, of North Yorkshire Police, said: “A loss of concentration of just a few seconds can cause permanent or even fatal injuries.
“Motorists should remember the '10 and 2' rule when passing horses: maintain a two meter following distance and limit speed to 10 miles per hour.”
“North Yorkshire is a rural county popular with horse riders and cyclists, and there is a lot of wildlife and livestock that wander onto roadways, so it’s always important to plan for the unexpected.”
The crash happened on Westcroft Lane on February 12 this year. Apollo was being ridden by a female jockey when McGregory struck the horse's hind leg and it did not stop. The collision occurred with such force that the rider suffered whiplash.
Drivers who cause personal injury accidents must by law stop and provide their name, address and vehicle details to the victim.
Westcroft Lane is a straight road on the outskirts of Hambleton, with country lanes at either end.
