Authorities arrived at the Fort MacArthur residential military facility in the 200 block of West 29th Street in San Pedro around 2:30 a.m. and found the mother and daughter suffering from stab wounds allegedly inflicted by the woman. Police say they were both in critical condition at that time. The child was slashed on her neck and wrists, police said.
The woman, 49, and her daughter were taken to County Harbor-UCLA Medical Center, where the girl died a few hours later.
Officials said the death is being investigated by the LAPD's Abused Child unit.
Fort MacArthur is an administrative center and residential community for the U.S. Air Force.
The identities of those involved have not been released.
AP contributed to this report.