Children and a 30-year-old man are among the gunshot victims, the Redding Record Searchlight reports.
The suspect reportedly started opening fire at a home, then moved to an elementary school, authorities say.
About 100 law enforcement personnel are examining at least five scenes of interest in Rancho Tehama, Johnston said.
It was also not immediately known if the shooter was counted among the people killed.
The shooting was first reported around 8:15 a.m. PT.
A spokesperson for the Tehama County Sheriff's Office said: 'We had multiple shots fired. According to local law enforcement, there were "multiple victims in multiple locations".
He heard there were people injured, but those were unconfirmed reports.
Rancho Tehama Elementary is reportedly now in lockdown. Rancho Tehama is southwest of Red Bluff.
"Our doors are locked", she said.