The "much-loved" female cat, Wowzer, was found dead by its owner near the family home in Carnoustie, Angus, after it had been missing for almost 48 hours.
Staff from animal welfare group the Scottish SPCA examined the previously healthy seven-year-old pet and discovered an airgun pellet.
Police have been carrying out door-to-door inquiries and appealed to anyone with information to contact them.
The cat was found on a grassy embankment on the south side of Barry Buddon Burn, near a footpath that runs by houses in Macdonald Smith Drive. It was shot between 6pm on Thursday and 1pm on Saturday.
The cat's owner, who did not wish to be named, said: "To have your cat die is bad.
"But then to have it confirmed that someone has maliciously targeted it with an air rifle - we are all just devastated."