Police say they were called to the baby's home about a dog attack late Sunday.
The newborn died at a hospital.
State Department of Children & Families spokesman John Harrell tells The Florida Times-Union that the state agency is working with police to investigate whether the baby was being supervised and whether the dog previously showed aggressive behavior.
"Our investigation will reveal if the incident was abuse, neglect or an accident," said the DCF spokesman.
The father said the family raised the pit bull since it was a puppy and that the dog never showed any signs of aggression toward anyone in their family.
"I want parents to know ... don't think you'll be quick enough," said the father. "It can happen in the blink of an eye."
The young, red pit bull was turned over to Jacksonville Animal Control and Protective Services, then euthanized at the request of the family.