Officers were told one of the animals involved was a Pitbull terrier type.
The incident happened at around 1pm yesterday in Topping Street, close to the Iceland food store.
One eyewitness told The Gazette: “The dog grabbed a smaller dog, a Jack Russell type.
“It had the dog by the neck and was shaking it like a rabbit.
“It was shocking to see.
“The little dog had just been tied up outside the shop.
“The police turned up and got them apart.”
Lancashire Police confirmed officers had attended the incident but could give no details on the breed of dog involved.
A spokesman said the animals had been separated and investigations are continuing.