The fire has burned between 30 and 40 acres of dry brush at Getty Center Drive above Sunset Boulevard west of the 405 freeway, according to Los Angeles City fire spokesman Eric Scott.
CHP officials are considering shutting down a portion of the 405 freeway. Sepulveda Boulevard has been closed between Sunset Boulevard and Mulholland Drive, near the Skirball Center.
Officials at the Getty Center say they are evacuating staff and visitors from the complex as a precaution.
Getty spokesman Ron Hartwig says an estimated 800 employees are working at the site.
It's unknown how many visitors are at the museum, but video from the scene shows dozens of people lined up outside the museum waiting to board trams.
Its estimated 3,000 visitors were at the museum.
Once everyone is out of the area, they will shut down the tram system, Hartwig says.
Mt. St. Mary's College, which is located about a mile west of the Getty Center, has also ordered evacuations.
Classes are not currently in session, but 100 staff members and about 200 people who were attending a conference at the school are being evacuated, according to officials at the school.
The fire is not threatening any structures, but evacuations are underway as a precaution.
About 250 firefighters are battling the blaze along with at least four helicopters.
Firefighters are getting water from the Stone Canyon Reservoir.
The Getty Center is perched on the brush-covered Santa Monica Mountains above the west side of Los Angeles.