A two-year-old girl has undergone surgery after a dog bit her on the face at a dog park in Sydney's inner west, police say.

The dog, which police said was believed to be a bulldog, has been put down following the incident at in Sydenham on Saturday night.

One man who claimed to have witnessed the incident said it occurred in a designated off-leash section of the park, which was fenced off.

Police said the girl was with her mother at the park, on Unwins Bridge Road, about 7.30pm on Saturday when she was bitten by the dog, which was not on a leash at the time.

"[The girl] sustained serious injuries to her eyelid and was treated at the scene by NSW Ambulance Paramedics before being taken to the Sydney Children's Hospital at Randwick for surgery," police said.