The accident happened just after 8 a.m. Thursday morning at Jackson and Kings Canyon.
Police say the small motorcycle, also known as a pocket bike, was headed southbound when it could not stop and hit a pick-up truck westbound on Kings Canyon.
The father and son suffered head injuries and are in the hospital.
Police say they were not wearing helmets and the bike did not have any brakes.
The mother of the boy says he was late for school and needed a ride. She picked up the bike from the scene.
Police say the pocket bike is not legal on city streets and the driver pick-up truck will not be cited.