St Louis County police said an officer had opened fire yesterday after coming under "heavy gunfire," and pictures on Twitter showed at least two cars with bullet holes.
Local media reported that one person had been taken to the hospital.
Demonstrators had taken to the streets to mark the anniversary of 18-year-old Michael Brown's death in a fateful encounter on August 9, 2014 with officer Darren Wilson.
Sunday's day of remembrance had been peaceful until a handful of protesters grew rowdy later in the evening. At least one shop was looted in the hours ahead of the gunfire, which occurred shortly after 11:00 pm (0400 GMT).
A crowd of about 300 people had gathered earlier to mark the anniversary, during which they observed four and a half minutes of silence and released two white doves.
Many in the crowd wore T-shirts emblazoned with Brown's portrait and the words "Choose Change." Others carried signs, including one that read: "STOP killing black children."
Brown's father, also called Michael, said he was grateful so many people had turned out for the march.
"If it wasn't for y'all this would be swept under the carpet. So I just want to give my love out to y'all," he said to the crowd.
In New York, dozens of people gathered at Union Square to hold a vigil for Brown in solidarity with Ferguson and to call for ongoing demonstrations against police killings of minorities.
One year on, black leaders say they have witnessed a dramatic change in American attitudes toward race, but see little action by lawmakers to enact policing reforms.
Yet another high-profile shooting occurred Friday, when a Texas police officer fatally shot 19-year-old unarmed college football player Christian Taylor after he drove his vehicle through the front of a car dealership.
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