The captain was transported to a hospital, LAFD spokesman Erik Scott told The Times. A second captain and another firefighter were also injured and taken to hospitals.
All three received injuries that were not life-threatening, the LAFD said.
Flames tore through the roof of the three-story home and thick clouds of smoke billowed into the sky as firefighters battled the blaze, according to television news footage.
The six-bedroom Tudor-style house is in the 4400 block of Balboa Avenue in the hills northeast of the Encino Reservoir, KTLA-TV Channel 5 reported. A tennis court was next to the home, which was at the end of a long private driveway, aerial video showed.
The home is at the end of a cul-de-sac in a hilly area of similar upscale residences. The cause of the blaze was under investigation.