The order included the Stough Nature Center, the Burbank Police Department said.
There were no immediate reports of injuries in the so-called Wildwood Fire, which broke out shortly before 4 p.m. near the police department's firing range and training facility and spread to the hills above Sunset Canyon Drive.
At least eight Burbank Fire Department units contained the blaze by 6:30 p.m. with assistance from the Los Angeles County Fire Department.
All roads in the evacuation area except Wildwood Canyon Road are expected to remain closed overnight, police said.
The cause of the fire was unknown.