The woman was taking her pup Minnie for a walk in Graves Park on Tuesday, June 18, when it was approached by two other dogs.
She said that Minnie was approached by a Brindle Boxer dog and a black Staffordshire Bull Terrier.
The boxer, which was not on a lead, then attacked Minnie before the owner rushed over to help.
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However, the Staffie then attacked Minnie whilst on its lead before the owner fled back to his car.
Following the attack, Minnie was rushed in for emergency surgery and is now recovering at home.
South Yorkshire Police said they investigated the issue and said they do not believe, at this stage, that a criminal offence has occurred.
Minnie’s owner has now issued an urgent warning over the ‘dangerous dogs’, calling on other pet owners to stay aware.
She wrote: “Dangerous dogs warning in Graves Park. My dog has had surgery after being attacked.
“She has been attacked by a brindle boxer dog and a black Staffie dog in Graves Park. The owner is a stocky, white, male, aged late 50's - early 60's.
“The Boxer dog was not on a lead and attacked my dog. The Staffie dog, on a lead, then attacked my dog when the owner came over. There was also another small, white dog which did not attack.
“Owner drives a white car. He ran off back to his car after the attack.
“The police are interested in the identity of this man. Please call 101 and quote crime reference number 417 on 18/06/19. Alternatively, please private message me details.
A South Yorkshire Police spokesperson said: “We received a report of a dog bitten by another dog in Graves Park, Sheffield, at 1.20pm on Tuesday 18 June.
“An officer has looked into the matter, and the circumstances of the incident does not suggest at this stage that a criminal offence has occurred.
“We would urge all dog owner to ensure their dogs are kept under control in any public place.”