The attack happened near the Göta sailing club on the island of Långholmen at about 10am, and boat owners called the police.
“It bit off one of its hind legs, leaving it hanging off,” said Tommy Ekheden of Stockholm police.
Police sent a wild animal expert to the scene. A policeman destroyed the badly mauled deer with his revolver.
Neither the dog nor its owner have been found. The owner was not seen by witnesses at the time of the attack.
According to witnesses the dog was a Rhodesian Ridgeback, a breed of hunting dog. Ridgebacks, which as the name suggests are native to southern Africa, can grow to be up to about 70 centimetres tall when on four legs, and weigh about 35 kilos.