The shooter himself has been killed by police and several victims are now being treated at a local hospital.
The elementary school is located on the outskirts of Corning, an olive oil-producing town of around 8,000 people about 100 miles (160 kilometers) north of the state capital Sacramento.
The shooter is understood to have been killed by law enforcement authorities. Mercy Dignity Health confirmed that the hospital has received three patients.
Officials in Tehama County say they're investigating at least seven crime scenes, one of which is an elementary school.
One student was injured at the school and another child was shot while driving with a woman, who also was wounded, Sheriff Johnston said.
The violence started with an apparent domestic dispute, according to neighbors, and spread out with the suspect "randomly picking targets", Johnston said.More news: Indian students' flow to U.S. grew by 12%, a three-year low
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Multiple shots were fired at the school and he was aware of at least three people killed, he added. The gunman was shot by officials, according to the sheriff's department.
Brian Flint told local media his neighbor was the shooter and had stolen his truck.
There were a total of 10 people injured, and Tehama County Superintendent of Schools Rich DuVarney said no students or staff at the school were among the fatalities.
In a statement, California Gov.
After the shooting, Johnston said police recovered a semi-automatic rifle and two handguns believed to be used by the shooter. "We offer our condolences to the families who lost loved ones and unite with all Californians in grief".