The Getty Fire started near the Getty Center arts complex and spread to about 500 acres (202 ha), close to some of the city's most expensive homes.
California's governor has declared a state-wide emergency as wildfires continue to rage in many other areas.
NBA star Lebron James was among those forced to flee the LA fire.
LA Mayor Eric Garcetti announced he would sign an emergency declaration to draw more resources to fight the Getty fire.
Some 3,300 homes are in the mandatory evacuation zone.
The wildfire is threatening LA's affluent Brentwood neighbourhood, and a local resident told the LA Times he was debating whether or not to leave, and which car of his two cars should be left behind.
"I have to figure out what I'm going to do with my Ferrari," the 47-year-old man said.
Meanwhile, wildfires are continuing to sweep through northern California.
Some 180,000 people have been ordered to leave homes, with roads around Santa Rosa north of San Francisco packed with cars as people tried to flee.
All schools in Sonoma County were closed for Monday and Tuesday as tens of thousands of homes remain under threat.
The biggest blackouts in the state's history have already left a million people without electricity. Power companies are trying to stop damaged cables from triggering new fires.
Another million people have been told they could lose supplies.
The main evacuation order in the north encompasses a huge area of Sonoma County, including Santa Rosa.