The collision resulted in extensive damage to the car. The driver suffered minor injuries and was taken to hospital.
Because the horse was seriously injured, officers at the scene made the decision to put it down, the police spokesman said.
"A number of members of the public stopped and offered assistance to the driver of the car, and others stayed with the horse."
The owner of the horse spoke with police at the scene.
There are plans to interview him further, the spokesman said.
"Police are looking at whether charges may be laid in relation to the horse's owner. Police will also liaise with the City Council in relation to animal control issues."