Police officers received reports of a road crash on Brackenhirst Road, Glenmavis, at around 9.30am on Sunday, April 25.
It is understood that the horse was killed almost instantly after the car collided with it.
The female horse rider was taken to Wishaw General Hospital having suffered back injuries in the accident, her current condition is unknown.
A nationwide campaign by the British Horse Society is urging road users to be more aware of horse riders to prevent incidents like this continuing to occur.
In the last year alone, 1,010 road accidents involving horses were reported to the British Horse Society.
As a result, 46 horses died and 118 were injured.
80 per cent of the incidents occurred as a result of a vehicle passing by too closely to the horse, while 43 per cent of those were also due to a vehicle passing too quickly.
Advice includes slowing down to 15mph when you pass a horse and giving it at least a cars width of space if it is possible.
You should be patient, not sound your horn or rev your engine, and continue to drive slowly past the horse and rider.
The driver of the car which hit the horse in Airdrie on Sunday has been arrested.
A Police Scotland spokesperson said: “Officers were called to the report of a road traffic crash on Brackenhirst Road, Glenmavis, Airdrie at around 9.24am on Sunday, April 25, 2021.
"A car and a horse were in collision. As a result the horse was killed.
"The female rider on the horse at the time was taken to Wishaw General Hospital with back injuries. The driver of the car was arrested and will be the subject of a report to the Procurator Fiscal.”