The shooter drove away and continued his carnage before dying in a shootout with police.
Officials said they recovered a semi-automatic rifle and two handguns from the shooter.
"At this point the suspected shooter is deceased by law enforcement bullets", Tehama County Assistant Sheriff Phil Johnston told reporters.
Jeanine Quist, an administrative assistant with the Corning Union Elementary School District, says no one was killed at the school but a "number" of students were shot and wounded.
The school is now clear, and all other students have been brought to a safe location.
Several children have been transported to the hospital. Another was struck by a bullet, while in a auto with a woman, according to Johnston. It is unknown where officers found the man.
India's wholesale price inflation rises to 3.59 per cent
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The gunfire began around 8 a.m.in Rancho Tehama, near Red Bluff, about 120 miles northwest of Sacramento.
The nearby Rancho Tehama Airport was placed on lockdown.
Flint described living next to the gunman as "hell".
"The insane thing is that the neighbor has been shooting a lot of bullets lately, hundreds of rounds, large magazines", neighbor Brian Flint told USA Today. "This guy has been insane, and he's been threatening us and everything".
Flint says he had been shooting "hundreds of rounds" from large magazines. "I just feel like there maybe should have been more effort put into stopping things like this".
A person with the username Javier Figueroa tweeted that the shooting had taken place at his brother's school. A woman driving the truck was also shot; all three are being treated. They heard the shooting from about a quarter-mile away and immediately corralled all of the students inside and locked down the facility. "We offer our condolences to the families who lost loved ones and unite with all Californians in grief".