The blaze was reported just before noon in the 12900 block of South Vermont Avenue, near the Hollywood Inn Suites Hotel, according to the Los Angeles County Fire Department.
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Video showed huge flames coming out of the two-story building's windows and thick black smoke billowing into the air.
Three people suffered minor injuries and a firefighter - whose condition was unknown - was also hurt.
Some of the apartments had significant interior damage and four units were red-tagged. Authorities say 28 people were displaced and are receiving assistance from the Red Cross.
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About 75 firefighters worked to extinguish the flames in roughly 45 minutes.
The cause of the fire is unknown.