The man, who calls himself “Mad Dog”, was in a Christian mob who attacked a Muslim in the capital Bangui.
He said he had been “angry” because Muslims killed his pregnant wife, his-sister-in law and her baby.
At least 1,000 people have been killed since violence broke out in the Christian-majority country in December.
Tens of thousands have also been forced to flee their homes in the sectarian conflict.
“Mad Dog” told the BBC’s Paul Wood he had seen his victim sitting on a minibus and decided to follow him.
More and more people joined him until he was at the head of a mob of some 20 youths, he said.
They forced the bus driver to stop and dragged the Muslim man out on the street, where he was beaten and stabbed before being set on fire.
Footage of the incident shows “Mad Dog” eating the man’s leg.
According to eyewitnesses, no-one tried to intervene.
Some people in the Central African Republic wear amulets containing the flesh of men they have killed because they believe it makes them invincible. – extract from bbc.co.uk