The Los Angeles County Sheriff's Department says Santiago Palacios-Salgado shot his ex-wife on Christmas Day, when their two children were present in the home.
Their son, age 6, and daughter, 8, were present but not injured in the shooting, police said.
When deputies arrived to the home in the 9100 block of Rosecrans Avenue on Monday at 3:18 p.m., they found a woman dead of a gunshot wound at the home.
They also found a man, with one gunshot wound to the upper body, believed to be self-inflicted. He was transported to a local hospital and was considered to be in fair condition.
The man was later identified as Palacios-Salgado and on Tuesday he was arrested for murder as he continues to be treated at the hospital.