The nine-year-old was in the play area in Craigie Park, Ayr, when she was badly bitten by the animal.
She was rushed to Crosshouse Hospital, Kilmarnock, after the attack on Friday at 10.20am and was treated for bites to her arms and legs. The girl has since been released.
Officers have laun-ched an investigation to trace the dog's owner. The breed of the animal is unknown.
A spokeswoman for Police Scotland said: "At around 10.20am on Friday April 18 police were called to reports that a nine-year-old girl was attacked by a dog at Craigie Park in Ayr.
"It is believed the attack took place in the swing park area of Craigie Park. The girl was taken to hospital and treated for injuries to her legs and arms.
"Inquiries are ongoing to find the dog and its owner and officers are appealing for anyone who was in the Craigie Park area on Friday morning to contact them."