Officers initially responded to an assault call in the 7400 block of Hazeltine Avenue at 2:50 a.m., according to the Los Angeles Police Department.
The victim, a woman in her 70s, was transported to a hospital, where she was pronounced dead, the LAPD said. Neither she nor the suspect were immediately identified.
Witnesses said the man jumped too, then stomped and kicked the victim.
Investigators said the incident was apparently the result of a domestic dispute. The nature of that dispute was unknown.
Aerial video from AIR7 HD showed at least five police vehicles in front of an apartment building, whose three residential levels sit above a street-level parking garage.