The fire broke out Monday morning at the two-story building and quickly engulfed the structure with flames and smoke, the Los Angeles Times said.
"This was a well-involved, intense fire," Los Angeles Fire Department spokesman Erik Scott told the Times.
Thick smoke forced rescuers to use an infrared search device to find victims trapped in the structure.
Firefighters found a man critically injured with the device, the Times said, and he was taken to the hospital, where he was later pronounced dead.
Officials said it was unclear what caused the man's death.
Another victim was taken to the hospital with non-life-threatening injuries and three others were treated at the scene.
Firefighters said they cut a hole in the roof of the building to allow the dangerous buildup of smoke to escape.