The peacekeepers were attempting to carry out an arrest warrant issued by the public prosecutor in Bangui's PK5 district yesterday, said the spokesman, Hamadoun Toure.
"There was an exchange of fire. During the exchange we lost one peacekeeper and eight peacekeepers were wounded," Toure said.
He declined to disclose the target of the warrant or the nationality of the peacekeepers.
Central African Republic has been rocked by violence since the mostly Muslim Seleka rebel coalition toppled the president of a decade in 2013. Widespread human rights abuses committed by Seleka led to the formation of a Christian militia known as the anti-Balaka, who have targeted Muslims and sent tens of thousands fleeing to neighbouring countries.
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UN Secretary-General Ban Ki-moon condemned the killing in a statement issued yesterday night.
"The Secretary-General deplores in the strongest terms attacks against United Nations peacekeepers and calls for swift action to bring the perpetrators of this crime to justice," the statement read.
The UN peacekeeping mission took over from an African Union peacekeeping force last September. Toure said he believed that the latest peacekeeper death was "the seventh or the eighth" for the mission.