The badger was discovered by a member of the public in Southowram, Halifax on Saturday.
An X-ray of the animal revealed it had been shot.
West Yorkshire Police are now appealing for anyone with information about the shooting to get in touch.
PC Newsome, of West Yorkshire Police, said: "On Saturday, March 20, this poor badger was found dead in Southowram, with X-rays concluding he had been shot.
"Anyone with information should call 101 quoting reference number 13210145502."