The animal was struck on the A926 Kirriemuir to Alyth Road, near Reedie Farm Cottages on Sunday afternoon.
The driver of the offending vehicle then drove off but police say they would have been aware of the collision.
Tayside police is now looking to speak to anyone who saw the incident.
Anyone with information that could assist officers with their investigation, should contact Tayside police on 0300 111 2222, or speak to any officer.
Alternatively information can be passed anonymously via the charity Crimestoppers on 0800 555 111.