Reports claim it was a counter-attack by Islamic militants after the body of a Muslim was found dumped by the airport.
The country has been in the grips of violence since political problems took hold after the majority-Muslim Séléka group drove out President Francois Bozizé in a coup two years ago.
Thousands of people have been killed and thousands more displaced in the region since 2013.
More than 100 injured in the clashes in the capital Bangui.
During the clashes guns and grenades were used and it is being reported that the United Nations peacekeeping forces did not stop the fighting.
Dominique Said Paguindji, the country's security minister, said that the violence was caused by the Anti-Balaka Christian militant group, the Muslim Séléka group and supporters of the former president Francois Bozizé.
He said: "These armed groups don't subscribe to a logic of disarmament and want to split the country.
"All of these people have the same interest in wanting to see the transition ruined and the coming elections halted."
CAR will hold parliamentary elections in mid-October which are hoped to replace the current government.