The incident is believed to have happened at the toddler's grandparents' home. The child's father has been interviewed by police.
Ms Malcolm-Black said such tragedies happened quickly, so children needed constant close supervision.
Cars had huge blind spots and pre-school children were often not visible out the back window through a rearview mirror, she said.
Plunket had been working to educate families on the importance of closely supervising children around the home.
"Unfortunately, it's the time when key family members might be leaving or coming into a building, and young children are excited to see family members but don't have the [awareness] to be safe around vehicles," she said.
"Because they aren't so visible, it's really important that someone else makes decisions for them about where they should be when vehicles are moving."
Safekids director Ann Weaver said New Zealand had one of the highest rates of children being killed by cars in driveways, with an average of five a year.
Every two weeks a child was hospitalised with serious injuries caused by a driveway-related accident, Ms Weaver said.
There have been 23 child deaths as a result of driveway runovers since 2007.
Awareness campaigns had halved the number of driveway deaths in recent years, but as soon as the campaigns stopped the numbers came back up.
The most common victims were toddlers aged 1 to 3.
Parents needed to keep a look out for children, know where they were at all times and make sure one adult was responsible for children playing outside if a car was entering or being removed from the property.
Toddlers tended to run out of houses quickly, she said.
"People don't notice. They think they've seen them a minute ago but it only takes a few seconds and they're off.
"Supervision is the key issue but it's not the only recommendation. Really it's about trying to think about what they can do around their own homes and fencing off a safe play area and making sure the doors that lead out to the driveway remain closed and locked."
Ms Weaver said parents living in state housing could contact Housing New Zealand and ask for a safe play area to be installed on the property. APNZ
Fatalities
47 children have been killed in driveways since the year 2000
23 killed nationally since 2007
Simple steps
CHECK:
Count the kids before you manoeuvre. Make sure they are in a safe place with an adult.
Understand how big the blind zones are around your car. Driveway runovers can happen driving forward and reversing.
Keep cars locked and don't let children use driveways as play areas.
SUPERVISE:
Ensure a responsible person (not a group of kids) is actively supervising toddlers and young children.
SEPARATE:
Separate children from all areas used for driving. Install a childproof gate at doors or exits that lead to driveways.
If you're expecting visitors, ask them to park on the road or put up a barrier to stop them parking in the drive. Source: Safekids
