The shooting happened around 1:30 p.m. Monday at an apartment complex in the 16000 block of Cornuta Avenue.
Friends identified the victim as 26-year-old Kenia Buckner, a mother of three who braided hair and was going to nursing school.
A man who knows the former couple said he was inside the apartment when suspect Antowan Parker walked in with a gun and told him to get the children out of the house, "and he did what he did."
Parker is described as an African-American man who is 5 feet 9 inches tall, with brown eyes and black hair with braids.
Police said he should be considered armed and dangerous.
Anyone with information about the shooting or the suspect was urged to call the Los Angeles County Sheriff's Department's Homicide Bureau at (323) 890-5500.