The neighbour, who asked not to be named, said he ran outside as soon as he heard the woman's screams just after 2.30pm.
"She had the motorbike parked behind her - hit that and got out. Then she pushed the car forward. I didn't see the young fellow, but he was in front of the car. Then she just started screaming."
The man told the Herald that neighbours started running outside to see what was wrong, but he ran to call an ambulance.
"All the other neighbours had run over there and were assisting. But like all mothers, she wouldn't let him go."
He said the little boy was covered in blood which was pouring out of his head and nose.
It is not clear how the child got in front of the car.
The emergency services operator told the man to try to keep the woman calm and to try to get her to let go of her son to let him breathe, but she could not stop clinging to him.
"She only let him go when the ambulance got there."
The neighbour said the little boy was the mother's only child and that she lived with her partner, who was out at the time of the accident.
"That mother loved her baby, she goes everywhere with her baby and plays with her baby - it's just one of those tragic accidents," he said.
Another neighbour, Mihi Lee, said police were taking photos of the driveway yesterday afternoon.
SafeKids director Ann Weaver said an increasing number of children were being run over in driveways every year.
"There's around five deaths a year and every two weeks there's a child that's hospitalised as a result of the injury," Ms Weaver said.
"We estimate around 80 per cent of the incidents are from reversing and 20 per cent are from the vehicle moving forwards."
Ms Weaver said the victims were often between 1 and 3 years old.
People often didn't realise what they couldn't see when they got into the car, she said.
"There is a large blind zone of up to three metres around and if you look in the rear vision mirror it's up to 10 metres that you can't see at the back.
"So you can actually fit a classroom of children behind a car and the driver will not see them."
SafeKids was running a Prevention of Driveway Run Over Injuries campaign focused on raising awareness around human behaviour, vehicle design and property design, she said.
Drivers should always check the driveway before moving the car, she said, and should try to fence off the driveway area.