Authorities said the UN officer, a Kenyan national, had been caught trying to board a plane while carrying ammunition, although the incident comes amid mounting tensions between the UN bureau in the country and the Burundian government.
"The airport services found two magazines with 15 bullets as he was about to get on a plane. He argued that he had forgotten about them, but one doesn't make a mistake about this kind of thing," Burundi's foreign minister, Laurent Kavakure, told AFP.
There was no official comment from the UN office. One official, speaking on condition of anonymity, accused local authorities of "taking revenge over the leak".
The incident came a month after another United Nations official based in Bujumbura was expelled over a leaked UN report that claimed the government was arming young supporters ahead of elections. The government also denied those allegations.
Tensions have been mounting in the small central-African nation in the run-up to presidential elections in 2015, when President Pierre Nkurunziza is expected to campaign for a third term in office, despite a two-term constitutional limit.