Liliana Carrillo, 30, is the only suspect in the deaths, LAPD officials said at a news conference.
The children were ages 3, 2 and 6 months, said Lt. Anthony Cato.
A law enforcement source told CNN that all three were stabbed. Police have not announced the cause of death.
No police report was available immediately and it is unknown if Carrillo has a lawyer.
The suspect’s mother discovered the children in the Reseda neighborhood, said Lt. Raul Jovel.
West Valley patrol officers responded to a call about “a possible death” in apartments there Saturday morning and found the children, LAPD he said in a tweet. Carrillo was arrested in Tulare County, in the community of Ponderosa, the department said. Tulare County is located about 160 miles north of the Reseda neighborhood in Los Angeles.
Officials did not cite any possible reasons.
Carrillo is also suspected of hacking a silver Toyota van in the Bakersfield area, the LAPD he said in a tweet during the search for her.