The child is said to be in a stable condition in hospital following the incident in Kilmarnock, East Ayrshire, at around 8pm on Tuesday night.
The pitbull, which did not belong to the boy's family, has been put down with the owner's consent, police said.
The boy was taken to Crosshouse Hospital in the town for treatment.
A 25-year-old man is to be reported to the procurator- fiscal in connection with an alleged contravention of the Dangerous Dogs Act 1991.
A police spokeswoman said: "Police Scotland received a report of a three-year-old-boy having sustained a facial injury after being attacked by a pitbull dog in a garden in Kilmarnock. The child was taken to Crosshouse Hospital, where he received surgery to a facial injury."
One neighbour said: "There have never been any problems with the dog, it was always fine as far as I could tell. The family are devastated. It's terrible what happened but it was just a horrible, horrible accident."
A series of measures to improve safety around dangerous dogs are being considered by the Government after a spate of incidents in recent years.
Universal microchipping, licensing and the wearing of muzzles in public areas are suggestions up for discussion in a public consultation, which was launched after First Minister Alex Salmond met with a group of parents whose children had been attacked by dogs.