The toddler was attacked at around 6pm on Saturday when the dog grabbed her ankle and dragged her to the ground. Her frantic mum tried to pull the animal off her and was bitten on the hand.
A man in his 30s eventually grabbed the dog and ran away from the scene.
The little girl was taken to Paisley's Royal Alexandra Hospital and later to Yorkhill Hospital in Glasgow where she was treated for foot and ankle injuries.
Inspector Alison Kennedy of Strathclyde Police appealed for information about the dog and its owner.
"This was no doubt an extremely frightening experience for a mother and her child and it's imperative we trace the dog and its owner. I would like to appeal to people who may have been in the park at the time of the incident to get in touch with us," she said.
She also appealed to people who walked their dogs locally to contact the police if they think they recognise the description of the man or the dog.
The dog is described as being a 'pitbull-type' and the man who pulled it off the child was white, in his 30s, with a slim build, about 6ft tall with short, dark, curly hair.