All three children were believed to be under the age of 5, police said.
Police did not confirm a motive or a cause of death, but multiple local media outlets report the children were stabbed to death.
Police discovered the bodies of the children while responding to a call about a possible death in an apartment along the 8000 block of Reseda Boulevard.
The mother, 30-year-old Liliana Carrillo, was taken into custody later Saturday in the Ponderosa area of Tulare County more than 200 miles away, in Central California. Police said Carrillo allegedly stole a silver Toyota pickup truck in the Bakersfield area before she was arrested.
“She is considered the sole suspect in this case,” the Los Angeles Police Department said.