The incident occurred as about 10 Muslims were lynched when Christian protesters decided to avenge the killing of their people by ex-Seleka rebels who are currently in power, a security source said.
Colonel Michel Narkoyo, the head of the national gendarmerie, said out of the 10, five were members of the same family while five were killed in the same locality where two French soldiers were killed on Monday.
Christians in Central African Republic have been accusing Muslims of colluding with the ex-Seleka rebels who took over power in March 2013, and who have been terrorising and killing Christians since then.
Having been disarmed by the French troops currently on the ground in Bangui, the ex-Seleka fighters now find themselves helpless against Christians who have linked up with self-defense militia calling themselves anti-Balakas.
The latter had taken up arms to fight against the new regime in Bangui.
The interim government led by Michel Djotodia has accused deposed President Francois Bozize of using the anti-Balaka militia to destabilise the country.
Over 600 people were killed in the violence during the past week, the UN's refugee agency said Friday.