The shooting began at 23:20 local time on Wednesday about 40 miles (65km) north-west of Los Angeles, police say.
At least 200 people were reportedly inside the Borderline Bar and Grill, which was hosting a university student night, at the time of the attack.
Officials say the suspect, who has not been identified, was found dead inside.
They have not yet confirmed any motive behind the attack.
President Trump tweeted on Thursday morning to say he been briefed on the shooting, describing it as "terrible", and praising the bravery of the police officers involved.
How did the shooting occur?
A college country music night was under way when the suspect, apparently dressed in black, entered the bar and opened fire.
Reports say the suspect may have used smoke grenades and at least one weapon, described as a semi-automatic handgun by witnesses.
A injured man told local television channel KTLA: "We just dropped to the ground, we heard a lot of screaming. My friend is the DJ so she cut off the music, we just heard a lot of mayhem."
Another witness from inside, Teylor Whittler, said: "I was on the dance floor and I heard the gunshots, so I looked back and then all of a sudden everyone screamed: Get Down!"
"It was a huge panic, everyone got up, I was trampled, I was kind of left on the floor until some guy came behind me and grabbed me and dragged me out."
People reportedly escaped the bar by using chairs to break windows, while others reportedly sheltered inside the venue's toilets.
What have police said?
Ventura County Sherriff Geoff Dean described the scene inside the bar as "horrific" and said there was "blood everywhere".
He said first responders arrived just three minutes after the first emergency calls from the venue were made.
Ventura Sheriff's Sergeant Ron Helus, who later died in hospital, had tried to enter the active scene with a local highway patrolman when he was shot several times.
The husband and father-of-one had been a policeman for 29 years and was due to retire next year.
"It saddens us all and tears at our emotions. He died a hero. He went in to save lives, to save other people," the Sherriff said.
Police say they recovered a handgun inside the bar and found the suspect dead inside.
They believe he may have taken his own life but have not confirmed this.
Who are the other victims?
It is not yet clear who the other 11 victims inside the bar are, but the Wednesday night country music event is popular with local university students.
https://www.bbc.com/news/world-us-canada-46135459
