The blaze was reported about 5:45 a.m. at a four-story structure in the 2900 block of Sunset Place, according to the Los Angeles Fire Department.
The flames started in one unit and then spread to one above. The two units were damaged by flames before being extinguished by firefighters within 40 minutes. Two other units were damaged by smoke and water.
The 56,577-square-foot building has 72 units.
"All these people in these 72 units were able to get out and stay out and let firefighters do their job," said LAFD Capt. Erik Scott: "It really helped us to ensure there were no civilian injuries."
Many residents said they did not hear any alarms, but were simply warned to evacuate by the yelling of other tenants.
"The smoke came all the way down to our unit and something should have alerted us that something was happening," said building resident Suza Khy.
The building was equipped with functional smoke alarms but not fire sprinklers, Scott said.
One resident said she sprained her ankle while running down a stairwell to safety. The two injured firefighters were transported to a hospital with burns that were described as minor but painful.
Residents say the fire generated a tremendous amount of smoke and flames.
"There was a huge fireball coming out the front. It was really crazy," said resident Dante Armstrong.
Red Cross volunteers also responded to the scene, where they were assisting residents of the damaged apartment units.
The cause of the blaze is under investigation. Residents were later allowed back inside the building.
#StructureFire; 5:45 AM; 2900 W Sunset Pl; #MacArthurPark; 4 story apartment building. KNOCKDOWN: 106 FF in 40 min. Fire extended to 2, 3rd floors & attic. @LAFD conducted thorough search. No civilian injuries.— Erik Scott (@PIOErikScott) November 25, 2017
2 #Firefighters suffered minor burn to ears. Cause under invest. pic.twitter.com/zYdfhSlWHR