The gunman remains at large, and a large-scale manhunt is underway.
Police say eye-witnesses have told them the assailant is aged between 30 and 50 years of age, and of Asian appearance.
They are also investigating whether the same man was involved in a separate incident at another dance club in the neighbouring city of Alhambra about 20 minutes after the first.
The Los Angeles County Sheriff's office has released a "wanted" poster, which describes the man as wearing a black leather jacket, a beanie, and glasses. It says the man is "armed and dangerous".
Sheriff Robert Luna, says police are using every resource available to arrest the suspect as soon as possible.
Detectives (are) looking at multiple locations, multiple clues. And I know how hard they're working. In regards to the firearm, obviously, there were multiple rounds fired at the first location where we have all the victims and survivors. We don't know how many rounds were fired. Different weapons have been described. In regards to the specific weapon, we don't believe it was an assault rifle at this time but again, that's part of the investigation.
Monterey Park is a city of about 60-thousand people, that's 11 kilometres from downtown Los Angeles.
The area is home to a large Asian population, with U-S Census data suggesting as many as two-thirds of residents are of Asian descent.
According to not-for-profit online site, the Gun Violence Archive, there have already been 34 mass shootings in the U-S this year, with 58 people killed and 145 injured.
