Dozens more have been injured and about 50 shops burned down.
The fighting took place in the mainly Muslim PK5 district of Bangui, an area often troubled by violence.
The clashes started when shopkeepers fought back against a local militia which has been trying to force them to pay taxes.
Ongoing violence since a rebel group seized power in 2013 has forced more than a quarter of the CAR’s 4.7 million people to flee their homes.
The UN mission in CAR, known as Minusca, has sent a rapid reaction force to the area to try and control the fighting.
Minusca spokesperson Biliaminou Alao told the BBC’s Focus on Africa that the outbreak of violence started when an armed militiaman, who wanted to dictate the price of some goods, was stabbed to death by a trader.
“We have decided… to establish a temporary base in that area… so that we can start discussion with local leaders to find ways to stop the crisis,” he said.
The UN mission did not say how many people died but said there were “dozens of victims”.
The UN mission also urged both sides to “show restraint to avoid a new escalation of violence, with disastrous consequences for the civilian population”.
Following years of unrest and bad governance, the CAR is one of the world’s poorest countries.
Two-thirds of the population needs humanitarian aid, according to the UN.
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