The firefighter is expected to survive after suffering a facial injury, according to the Los Angeles Fire Department.
Aerial video from AIR7 HD showed flames rising from the 30,000-square-foot building in the 700 block of Pico Boulevard after the roof collapsed shortly before 5 a.m.
The inferno was extinguished in 47 minutes by 117 firefighters and did not spread to adjacent structures, the LAFD said.
The cause of the incident is under investigation.