The animal was found dead in a field near the town of Lockerbie, on September 21.
Red squirrels are protected animals as part of the Wildlife and Countryside Act 1981, and it is a criminal offence to injure or kill a red squirrel.
A man carrying an air rifle was seen in the nearby area at Gallaberry Road, near the Torwood Road.
Police and the Scottish SPCA are appealing for help in tracing those responsible.
An undercover Scottish SPCA investigator told the BBC: “A male suspect was seen in the area cycling with what is believed to have been an air rifle or similar in a gun slip worn over his back.
“He is described as being of stocky build and was wearing a camouflage hat and jacket.”
Scotland is home to an estimated 85 per cent of the world’s red squirrel population.