A man has killed a woman in front of her 12-year-old son after the pair laughed at him in the US.

Denise Berry, 44, was driving with her son in Hawthorne California on Wednesday (Thursday NZT) when he pointed out a man whose feet were hanging out of his car window, Los Angeles police officer Dave Coleman said.

The mother and son shared a chuckle. At some point, the boy made eye contact with the man.

"That's not a reason to go out and murder someone," Coleman said.

The man, who has been identified as Robert Washington, 38, was driving a Cadillac.

Washington continued driving and followed Berry's Mercedes-Benz until she spotted a police officer.

Berry, who was a mother of three, told the officer she was being followed. The officer asked Berry to pull her car in front of his police cruiser so he could help her.

That's when the Cadillac pulled up next to Berry's car, and Washington began firing, police said.

The officer jumped out of his patrol car and shot Washington, killing him.

Berry was shot and died. Her son was hit too, but was able to run away. He is in a stable condition at hospital.

"He watched his mother murdered in front of him," Coleman said. "That's horrific."

Stanley White, 24, and Brandon White, 19, who were passengers in Washington's vehicle, were also arrested, police said.

Investigators say there is no indication Berry and Washington had been in contact prior to the shooting on Wednesday. Coleman said Washington had a lengthy criminal history.