Police were called to the dance hall in Monterey Park at 10.22pm (local time), a city of about 60,000 people which is 16km east of LA.
Captain Meyer told media there was no known motive and no description of the shooter – who remains at large but is believed to be male.
He said it was “too early in the investigation to know if this was a hate crime”.
The weapon used is also unknown, with police only able to describe it as a “firearm”.
Police are scouring CCTV to look for more information that might help identify the attacker.
The 10 victims in hospital have injuries ranging from critical to stable.
Earlier in the day, thousands of people attended the festival. Tomorrow’s planned festival has been cancelled by authorities.
Seung Won Choi, who owns the Clam House seafood barbecue restaurant across the street from where the shooting happened, told the Los Angeles Times that three people rushed into his business and told him to lock the door.
The people also told Choi that there was a shooter with a machine gun who had multiple rounds of ammunition on him so he could reload. Choi said he believes the shooting took place at a dance club.
The newspaper reported that the shooting happened after 10pm local time.