People looted shops, vandalized cars and stores, and set a building alight on Sunday as police tried to block off access to several areas of St Louis.
Police say Michael Brown, 18, was shot on Saturday afternoon in Ferguson, a mainly black suburb of the city.
He was shot several times after a struggle in a police car, they said.
The rioting erupted late on Sunday after thousands of people attended a candlelight vigil for Michael Brown.
County Police Chief Jon Belmar said the shooting occurred after the officer encountered two men, including Michael Brown, on a street in Ferguson, the Associated Press news agency reports.
Jon Belmar said one of the men pushed the officer back into his squad car and a struggle began.
At least one shot was fired from the officer’s gun inside the police car, Jon Belmar said.
Authorities say they are still trying to clarify exactly what happened inside the vehicle.
The officer involved has been with the Ferguson police department for six years, and has been placed on paid administrative leave, Jon Belmar said.
Mayor James Knowles said he understood that people “want to vent their frustrations. We understand they want to speak out”, but he added: “We’re going to obviously try to urge calm.”
Michael Brown’s mother, Lesley McSpadden, said her son had graduated from high school and planned to go to a local college.
The killing has drawn comparisons by some civil rights leaders with the 2012 killing of 17-year-old Trayvon Martin by a Florida neighborhood watch organizer who was acquitted of murder charges.
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