The incident happened shortly before 7am today on the B6265 between Studley Roger and the Galphay turning.
The Charolais beef bull was found injured in the road.
The driver of the vehicle, which is believed to be a beige coloured Kia Picanto, left the scene without stopping.
North Yorkshire Police hope to determine the full circumstances surrounding the incident.
A spokesperson said: "In particular, we are appealing for information about the beige vehicle that failed to stop.
"Anyone with information that could assist the investigation should contact us on 101, select option 2, and ask for Rob Roberts.
"You can also email [email protected]
"If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111."