South Yorkshire police said the two-year-old girl was injured in Rawmarsh, shortly before 10am yesterday.
Police said the dog, believed to be a family pet, had been on a lead when the attack happened.
The victim had been with a woman and the dog at the time.
A police spokesman said: “The girl was taken by ambulance to Rotherham District General Hospital suffering from what are believed to be serious injuries to her head and to her leg.
“She has since been transferred to Sheffield Children’s Hospital.”
The dog has been taken to a secure kennel facility whilst police inquiries continue into the circumstances surrounding the incident.
Officers described the girl’s condition as stable and not life-threatening.
The attack came on the day the Government announced proposals for life jail terms for owners of killer canines.
It began a consultation following pressure from a number of families campaigning for tougher sentences after a relative was killed by dogs.
Michael Anderson’s step-daughter Jade Lomas-Anderson was savaged by four dogs - believed to be two bull mastiffs and two Staffordshire bull terriers - as she was visiting the home of a friend near Wigan, Greater Manchester, in March.
No prosecutions were brought against the owner of the dogs that killed the 14-year-old, as the incident occurred on private property and they were not illegal breeds.
Mr Anderson, 34, welcomed the plans but said more needed to be done to prevent attacks.
“We are still going to be campaigning,” he said.
“It’s about early prevention, it’s about stopping it happening in the first place.
“It’s a bigger problem than most people think it is. Nearly a quarter of a million dog attacks last year alone, 6,500 hospitalised, there’s a bigger picture.”
For owners whose dogs kill their victims, life imprisonment is an option, while 10 years is the maximum term suggested for injuring a person or killing an assistance dog, like a guide dog for the blind.
The new consultation will run to September 1 and will be used to inform recommendations put forward in the Anti-Social Behaviour, Crime and Policing Bill.
Some 16 people have been killed by dangerous dogs since 2005, including Jade.