The incident was reported shortly before noon at a shopping center in the 39800 block of North 10th Street West, according to the Los Angeles County Sheriff's Department.
A suspect was taken into custody. Details about the suspect were not available.
In a news release, the Sheriff's Department said a woman was found dead at the scene. The man was taken to a hospital, where he died of his wounds. Both had multiple stab wounds.
Neither victim was immediately identified. Whether they were targeted or attacked at random was unclear.
Authorities say no weapon has been found.
Anyone with information about the incident is urged to contact the sheriff's Homicide Bureau at (323) 890-5500.
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