The`18-month-old boy was found in a car seat in the back of a silver Volkswagen Golf when it was dumped in a street after the driver jumped out to evade arrest.
South Yorkshire Police said the car was still moving when the driver fled.
An officer spotted the car in Rotherham and began following it when the driver 'started to make off'.
The driver 'jumped red lights' and broke the speed limit during the pursuit near Rotherham town centre at around noon yesterday.
A police dog tracked the driver down and an investigation is now underway.
The car was uninsured and the driver did not have a licence.
A South Yorkshire Police spokesman said: "This Volkswagen Golf was seen by one of our officers driving around Rotherham.
"Before the officer asked for the vehicle to stop, the vehicle started to make off.
"A pursuit ensued during which the Golf jumped red lights and reached speeds well in excess of the speed limit - all just before midday not far from Rotherham town centre.
"After a few minutes and while other resources were making their way to the area, the driver drove down a cul-de-sac and abandoned their car whilst it was still moving, albeit slowly. The only damage caused was to their wing."
The spokesman added: "The pursuing officer was surprised to find a seat in the rear of the car.
"They were even more surprised to find an 18-month-old little boy in it, thankfully uninjured, happily rubbing a slice of pizza all over his face.
"The driver did their best to escape, but unfortunately for them, police dog Bruce and his handler were nearby.
"Bruce tracked the driver over fields and detained them until his handler could arrest them. Unfortunately the driver thought it was a good idea to try and fight Bruce off. Bruce won. The driver has had a trip to hospital for their injuries treating.
"!Most infuriatingly of all, it appears as though the reason the driver didn't stop was that their car was on false plates to hide the fact they didn't have any insurance or an appropriate driving licence.
"That someone would put themselves and others at risk for something like that always beggars belief. That they would do it with their baby in the car is unbelievable."