Three people were also wounded in the clashes in the rebel stronghold of Bambari, rebel spokesman Captain Ahamat Najat said.
The former French colony has been gripped by violence since Seleka, a coalition of mostly Muslim rebels and some fighters from neighbouring Chad and Sudan, seized power in March 2013.
Their rule was marked by abuses that prompted a backlash from the Christian militia. Violence continued after the resignation of Seleka leader Michel Djotodia as president in January.
Most Muslims have fled the south of the country in the face of violence, creating a de facto partition. Some members of the Seleka leadership have pushed for this to be formalised.
Around 2,000 French and 6,000 African Union peacekeepers are in the country but have struggled to help the weak transitional government.