The Long Beach Fire Department said the blaze happened in the 5500 block of Dairy Avenue before 7:30 p.m.
When crews arrived to the two-story apartment complex they found fire and heavy smoke billowing from the first floor.
Firefighters were able to knock the fire down at about 7:40 p.m. A body was discovered in a first-floor unit where the fire was believed to have originated.
During the blaze, officials said a family of five living in the unit above the apartment where the fire sparked had to flee to safety.
A 28-year-old man who jumped from the second floor balcony was taken to the hospital, according to the fire department. Officials didn't disclose the extent of his injuries.
The fire department said a 26-year-old woman, two boys, ages 9 and 7, and a 4-year-old girl were treated and released at the scene.
A 24-year-old woman who cut her leg on glass was also treated and released at the scene.
Officials said out of six apartment units, two sustained damage. The blaze remained under investigation, the fire department stated.