The goose was so beloved by residents during its life that it was featured on the village's welcome sign.
Gay Ayton, who has lived in Sandon for 20 years, told the Hertfordshire Mercury that the act was "spineless."
"It's really shocking. A lot of the villagers are feeling very sad – even though he was cursed as sometimes you couldn't post a letter without a stick," she said.
Police told The Guardian that they are investigating the circumstances surrounding the goose's death but may have to dig up its body to confirm the shooting.
"At the moment we cannot confirm if it has been shot or not because we would need a body to do that," a spokesperson for the Royal Society for the Prevention of Cruelty to Animals said. "A lot of rumors have been going around, but if we are able to identify someone down the line then we would do a joint interview with the RSPCA."
The goose was buried near the lake, as residents placed gifts near its grave including flowers and letters from local children.