Only the pilot and a woman passenger are said to have survived from the 22 people on board the plane.
The BBC's Joseph Benamsse in Bangui says the plane came down in a fish farming area and is not thought to have caused any casualties on the ground.
The plane left the Chad capital, Ndjamena, and was heading for Brazzaville in neighbouring Congo when it developed technical problems, according to aviation sources.
It crashed at 1200 local time (1100 GMT), coming down in the market district of Guitangola, four kilometres short of the airport.
The fire brigade is attempting to pull bodies out of the mud.
Looters
"I was afraid when I saw the plane coming down, and all of a sudden I heard a loud noise, and some parts of the aircraft flew into the air and fell in the mud," said Zara, a woman who watched the crash from her farm.
An airport worker told the French news agency, AFP, that he was not allowed within 300 metres of the crash scene.
"People were crying everywhere. There were thousands of people. I even saw people walking away with bits of the aircraft," the airport worker said.
The plane was carrying a cargo of onions, and some locals who came to see the crash have been making off with bags of the vegetables.
Hospital workers in Bangui are currently on strike.
It is not clear whether they will continue with their action, despite the plane crash.