Officers at the scene told the newspaper that about 30 shots had been fired.
He could not immediately provide information on the extent of the victims' injuries.
The bar's website says its hosts "College Country Night" every Wednesday.
Authorities urged the public to avoid the area.
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Police were responding to reports of an active shooter after several people were injured in a mass shooting at a California bar holding an event for college students early Thursday.
"We can't confirm the shooter is in custody at this point", Ventura County Sheriff's Office Capt. Garo Kuredjian said at a news conference.
This is a developing story, check back for updates.
Ventura County Sheriff's Office described the situation as a "very active scene".
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At least six people, including one officer, were injured in the shooting the Borderline Bar and Grill at about 23:20 local time on Wednesday. There was a massive law enforcement presence.
Witness John Hedge told ABC's 13WLOS TV station that said he saw a suspect throwing smoke bombs into the front of the restaurant.
People gathered near the scene of the shooting, hugging and crying as red and blue lights from police cars flickered in the background.
"The gunman used an automatic weapon and also threw in some sort of smoke bombs in to the crowd in the club", he said.
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Thousand Oaks is in Ventura County, about 40 miles from downtown Los Angeles.