On the morning of Sunday, June 23, two calves were discovered with what are believed to be crossbow bolts stuck in them.
A one-month-old calf was put to sleep at the scene, while a four-month-old calf which had been shot in its hindquarters is expected to survive.
The animals were discovered off Burnthurst Lane, near Princethorpe and the incident is believed to have occurred sometime between 7pm on Saturday June 22 and 10am yesterday.
Carol Cotterill, Rural Crime Officer, Warwickshire Police, said: "This was a despicable attack. We are particularly interested in hearing from anyone who was in the area over the weekend and saw anything suspicious."
Anyone with information should contact Warwickshire Police on 101 quoting incident 128 of 23 June 2019.
Alternatively information can be provided anonymously to the independent charity Crimestoppers on 0800 555 111.