Police have seized the dog after reports of the attack in Southend Park on Sunday (March 23) at 3.37pm.
Medics at the scene treated a child for dog bite wounds and they were taken to a hospital where their injuries were found to be non-life threatening.
No arrests were made after the incident but enquiries into how the injuries came to be are ongoing.
A spokesperson for Metropolitan Police Service said: “On Sunday (March 23) police were called to Southend Park at 3.37pm following reports that a child had been bitten by a dog.
“Officers attended the scene alongside the London Ambulance Service who treated a child for dog bite wounds. The child was taken to a near-by hospital, their injuries are non-life threatening.
“The dog was seized by police at the scene. There were no arrests, enquiries are on-going.”