The Scottish SPCA was alerted to the incident after the owners took their dead pet to the vet, who confirmed it had been shot with a pellet and had died due to the extent of its injuries.
The incident happened in the Turnberry Wynd area of Irvine, North Ayrshire, on Tuesday, March 2.
The Scottish SPCA is now working with local police on the investigation due to the involvement of a firearm and have appealed for information.
A Scottish SPCA special investigations unit inspector, who cannot be named due to undercover work, said: “Our thoughts are with the owners just now. This has been an incredibly upsetting and stressful time for them.
“The cat didn’t venture far from their house, so this has happened close to where the owners lived.
“We are asking anyone in the area who might know what happened to come forward.
“This was a deliberate attempt to kill an animal, which is a criminal offence punishable by law.
“This abhorrent act also shows a complete disregard for the life of an animal so we are asking pet owners in the area to be vigilant until we find the person responsible.
“We are working closely with Police Scotland to establish the circumstances due to the use of a firearm in the incident.”
Anyone with information is asked to contact the Scottish SPCA’s confidential animal helpline on 03000 999 999.