The crash occurred at 27th Street and MacDonald Avenue in Richmond shortly before noon when the child slipped away from his mother as she tried to put him in her car.
The child was transported to Oakland Children's Hospital in critical condition.
"We are also asking the public to help us out on this one. This is a child. A 3-year-old child," Richmond Police Department Lieutenant Felix Tan said.
Police released images of the suspected vehicle, a red and black Smart car. They are asking anyone with information on the accident to contact them.