Liliana Carrillo, 30, is the only suspect in the death, LAPD officials said at a news conference.
The children were between the ages of 3, 2 and 6 months, Lieutenant Anthony Cato said.
A law enforcement source told CNN the three were stabbed with a knife. Police did not disclose the cause of death.
A police report was not immediately available and it is unknown if Carrillo has a lawyer.
The mother of the suspect discovered the children in the Reseda area, lt. Raul Jovel said.
West Valley Patrol Officers responded Saturday morning to a call about a possible death at apartments there and found the children, LAPD said in a tweet. Carrillo was arrested in Tulare County, in the Ponderosa community, the department said. Tulare County is located about 160 miles north of the Reseda area in LA.
Officials do not name a possible motive.
Carrillo is also suspected of hijacking a silver Toyota pickup truck in the Bakersfield area, the LAPD said in a tweet during the search for her.