Officers tried to pull over a car with paper plates, believing the vehicle may have been stolen, authorities said.
When the driver refused to stop, police began a pursuit, Sgt. Barry Montgomery said.
He said the passenger got out of the car at some point and ran into the back of a house, where he was shot. The driver fled the scene and remained on the loose.
Montgomery said a weapon was recovered at the scene, but he would not say what it was or what led to the shooting.
The shooting drew several dozen people to the scene, angered that police had shot a black man. A small group of protesters blocked an intersection near the shooting scene Saturday night, with some waving signs that read "Black Lives Matter" and others shouting at officers in riot helmets, AP reported.
The demonstration is the latest sparked by a series of fatal shootings of black men by officers around the country. This past week, an unarmed black man was fatally shot by police in the San Diego suburb of El Cajon, triggering days of angry, sometimes unruly, protests. The fatal shooting of a black man armed with a knife by Pasadena, California, police Friday led to two mostly peaceful protests.
Relatives of the dead man in Los Angeles identified him as 18-year-old Carnell Snell Jr., and they said he was killed on the same street where he lived.
Trenell Snell, 17, said she was outside with friends when she saw her older brother running from police. She said she started running too, and that she hit the ground when she heard gunfire.
When she got up, her brother was on the ground, handcuffed, she said.
"At the end of the day, the cops came and shot my brother," she said. "Killed my brother."
Snell's mother told reporters she asked authorities to let her see the dead man to confirm whether he is her son, but they wouldn't allow her to do so.