The sheep was discovered by its owners in “great distress” several hours after it was shot.
Its injuries were so severe it had to be euthanised.
The culprits also caused extensive damage to hedges, crops and a gate before shooting the animal at some point between 10pm on Monday May 16 and 5am on Tuesday May 17.
The offence took place on land off Malton Road at Marton, near Sinnington.
Officers from North Yorkshire Police’s Rural Taskforce are investigating the incident, and are carrying out extensive enquiries in the area.
Police are appealing for anyone who knows anything about the incident, or saw any suspicious vehicles or people in the area to contact them as a matter of urgency.
Anyone who can assist the investigation is asked to email [email protected], or dial 101, select option 2 and ask for PC Neil Cholmondeley, quoting reference NYP-17052016-0054.
Alternatively, call Crimestoppers anonymously on 0800 555 111.