The girl, her brother, 10, and their mother were all taken to hospital after being mauled by the dog on Easter Sunday.
The dad told the Richmond and Twickenham Times that the dog had been off the lead when it ran out of the woods and attacked his daughter.
“I don’t know how my daughter survived it if I’m honest,” he said.
“It was like a shark attack, I’m amazed she didn’t lose her arm.”
Watch: Some Arizona pets testing presumptive positive for COVID-19
The dad said the dog bolted from the trees and lunged towards his daughter who panicked, sending the animal into a frenzy.
He said his wife tried to intervene but the dog sunk its jaws into her hand. In a desperate bid to stop the animal the dad kicked it but the dog started to run after his son.
“Finally, the owner ran over and jumped on the dog to control it, though it was clear he had no control over it,” the dad said.
“He tried to blame our children for running, but children deserve every right to run in a park without being mauled by a vicious dog.”
Police were called to the park at 5.44pm on April 4 to find the mum and her nine-year-old daughter suffering from deep bite wounds.
The dog had also bitten the girl’s 10-year-old brother on the arm.
London Ambulance Service treated all three before they were taken to hospital.
Three men and the animal were pictured just before the attack.
Anyone who has information or knows the men is encouraged to get in touch with police.
“Police are looking to speak to three males involved in a dog attack causing serious injury to victims in Bushy Park on Easter Sunday 4th April at around 5.30pm,” a Met Police Spokesperson said.
Watch: Rescued kittens have a blast on their first night at their sanctuary