A relative said the boy's grandmother was "distraught" as she contacted family with news of the youngster's death last night.
The boy and his family are from Napier.
When Hawke's Bay Today arrived at the scene of the accident yesterday a police cordon had been set up around the KFC carpark. Police were focusing attention on an area near the front entrance.
Inspector Hirone Waretini said the police Serious Crash Unit was investigating.
"This can be classified 100 per cent as a tragedy."
Police were speaking to the male driver of the car that had hit the boy, as well as the boy's parents and witnesses who were in the carpark at the time.
Eastern district police Senior Sergeant Greg Brown said KFC had advised police there was nothing on their cameras. "Although we will review those as part of our investigation," Mr Brown said.
The boy's name would not be released until all members of his family had been notified.
SafeKids Aotearoa director Ann Weaver said there were "blind zones" in cars that didn't allow for a person the size of a 2-year-old to be visible at all times.
She advised parents to keep young children "within arm's length" in carparks.
"It's terrible we have a tragedy like this that reminds us of the importance of being vigilant with children around cars."
The case was now before the coroner.
