Two other children and the mother were injured.
The car struck the family about 4:45 a.m., WCPO-TV, Cincinnati, reported.
Authorities said the female driver of the vehicle crossed double yellow lines, drove up onto the sidewalk and hit the mother and children.
The 3-year-old died shortly after being taken to a hospital. The other children and mother were being treated. No details were reported on their injuries.
The driver of the vehicle was in police custody. Officials said they believe alcohol may have been a factor in the crash.
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