She was transported to Auckland by road and was expected to be admitted to the paediatric intensive care unit.
Mr Adamson said police were investigating the incident.
It comes a week after Samantha Mauheni pushed her car over her 21-month-old son Kingston in a Gisborne driveway.
Miss Mauheni was trying to get a toy motorbike out from under the vehicle. She had reversed over the toy and when she went to get it out from under her back wheel, her car lurched too far forward. The 21-year-old did not know Kingston was in front of the car.
The toddler was rushed to Gisborne Hospital, but died a short time later.
According to statistics from Starship service Safekids New Zealand, a child is hospitalised every two weeks with serious injuries received from a vehicle driving on a private driveway.
The majority of drivers involved are close family members.
A further five children, on average, are killed annually in the same way.