Los Angeles police say the violence unfolded Wednesday night at a home in the 16200 block of Londelius Avenue.
The LAPD told Eyewitness News that detectives believe a woman in her 30s shot and killed her two children and her husband before turning the gun on herself.
The husband was identified as 31-year-old Khajag Basmajian. Investigators have not released the woman's identity or a motive.
The other victims were identified as Ella Basmajian, who was only six days old, and 2-year-old Alec Basmajian.
Neighbors struggled to process the loss.
A memorial of balloons, flowers and toys were placed outside the home Thursday where just 24 hours earlier, heartbroken family members sat on the floor in disbelief at the news.
"This is the kind of situation where you wonder why didn't the mother just take her own life and leave these people to live?" neighbor Judy MacKenzie said.
Another neighbor, Florence Barreras, who lives next door, said she did not notice anything unusual the night of the shooting. The last time Barreras saw her neighbor she was still expecting her new baby.
Police continue to investigate the case.