Police said the incident was reported yesterday evening at a house at Ruban Peiris Mawatha in Kohuwala.
The infant who was injured in the accident was admitted to the Colombo South Teaching Hospital and then transferred to the Colombo National Hospital where she later died.
Police said the accident occurred due to reckless driving by the girl's uncle.
The driver who is the brother of the infant's mother, who is a businessman was arrested after the incident and the vehicle was also taken into custody.