Officers and paramedics responded to a call from a woman who said she ran over her child in the 200 block Vista Way at about 10:05 a.m., according to Martinez police.
The boy, whose injuries were considered life threatening, was still under the vehicle when first responders arrived, police said.
A medical helicopter landed at John Muir Elementary School and airlifted the boy to Children's Hospital of Oakland, where he underwent extensive surgery.
A preliminary investigation revealed the mother had pulled her car on to the street to provide a battery jump to a commercial vehicle, police said.
When she pulled back into the driveway, she did not notice that her son had moved from the front yard into the path of her car.
Drugs or alcohol were not a factor in the collision, police said.
As of Sunday morning, the boy was on life support in an intensive care unit of the hospital, police said.