A member of the public found the animal in a case next to communal bins on Farquhar Road, Aberdeen.
The female German Shepherd was in very poor condition and very underweight, the Scottish SPCA said.
The animal welfare charity has launched an investigation and is appealing for information.
Scottish SPCA chief inspector John Carle said: "She was a female German Shepherd around 11 years old. A vet report concluded that she was in very poor body condition, although we have been unable to establish the cause of death."
The Scottish SPCA was told about it on April 30.