The Los Angeles County Fire Department said crews responded to the 3700 block of 106th Street at about 12:50 p.m.
The scene was located near Morningside High School, Monroe Middle School and Woodworth Elementary School. Morningside High School was placed on lockdown as precaution.
Inglewood police said a man and woman were attacked by their daughter's ex husband during a family-related incident.
The male victim was pronounced dead at the scene while the woman was rushed to Harbor-UCLA Medical Center in serious condition.
The identities of the victims were not immediately released by police.
Authorities said the suspect fled and got on the roof of a home near the crime scene. Hostage negotiators arrived and attempted to talk the man while SWAT members surrounded the area.
Air7 HD spotted the suspect on the roof as police stood below with guns drawn.
The man appeared to be gesturing to police with his hands and at one point removed his shirt.
After a long standoff, the man came down from the roof and was taken into custody at about 3:10 p.m.
Authorities said no one else was injured during the incident.
Anyone with information that could aid detectives in their investigation was urged to call the Inglewood Police Department Homicide Section at (310) 412-5246.