The shooter himself has been killed by police and several victims are now being treated at a local hospital.
The violence began at a home and ended at Rancho Tehama Elementary School, where one student was shot.
"We are cooperating with local law enforcement - we don't have any confirmed information at this point", but a statement from the superintendent will be forthcoming when they know more, she said.
"I know that we have (airlifted) a number of students", Assistant Sheriff Phil Johnston told the station. Enloe Hospital received four, according to hospital officials.
Mr Johnston said police were alerted to the shooting at around 8am local time (4pm GMT). Three people were being treated at a hospital in Redding, about 50 miles north of the shootings, Dignity Health Mercy Medical Center spokeswoman Marcy Miracle said.
The school has been cleared, he said, and all other students have been brought to a safe location.
Shots were fired at the school and some people were injured at the campus but no students or staff members died, Corning Union Elementary School District administrative assistant Jeanine Quist said by phone.
A female adult also in the truck was struck by gunfire as well, Johnston said.
A reporter at Action News Now described anxious parents trying to get to their children at Rancho Tehama Elementary. Police recovered a semi-automatic rifle and two handguns from the scene. Flint says he had been shooting "hundreds of rounds" from large magazines.
A witness told KCRA that the gunman stole his truck and shot and killed his roommate.