The Redding Record Searchlight said among the wounded was a six-year-old who suffered two gunshot wounds and another child shot in the leg.
Mr Johnston says the gunman was "randomly picking targets".
About 100 law enforcement officials responded to "multiple scenes, I can think of at least five scenes", after the shooting, he said.
Authorities have recovered a semi-automatic rifle and two handguns after the shootings in the rural subdivision described on its website as a "quiet private country community" where "the people are friendly and the pace is relaxed".
All other students have been brought to a safe location, he said.
He said the gunman was a neighbor and had "been shooting a lot of bullets lately, hundreds of rounds, large magazines".More news: Syrian drone intercepted after approaching Israeli airspace
Enloe Medical Center said it had four patients from the shooting - one adult and three children.
"We made it aware that this guy is insane and he's been threatening us".
In another recent fatal school shooting, a student opened fire at Freeman High School in Rockford, WA, on Sep.
"I know that we have Medivaced a number of students", Johnston said, referring to the use of helicopters for the emergency transport of victims to hospitals. The FBI confirmed to CBS News they are sending agents from Sacramento, Redding, and Chico to assist with the investigation.
Deputies received a report of shots fired at around 8 a.m.at Rancho Tehama Elementary school, said a Tehama County Sheriff's Official. "I don't believe it because I wake up, take my kids, feed them cereal and put them in the truck and says 'Let's go to school like a normal day'".
Living near the gunman was "hell", Flint said, and the man was a known felon who often harassed him and his neighbors.