The gunmen, who appeared to be linked to the mainly Christian anti-balaka militia, seized the woman from a van taking UN staffers to work in Bangui, the source with the UN's MINUSCA mission in the country said on condition of anonymity.
The abduction came a day after a French charity worker and a churchman were seized in an area of the city controlled by anti-balaka militia fighters.
The militia demanded the release of one of its leaders who has been arrested for crimes including murder.
"Unidentified armed men kidnapped on Tuesday a woman who works for MINUSCA after having stopped the vehicle in which she was travelling. A similar kidnap attempt failed just a bit earlier," said MINUSCA in a statement.
The country sank into chaos when the mainly Muslim Seleka rebel umbrella group seized power in the majority Christian state in March 2013, ousting President Francois Bozize.
A backlash from the mostly Christian or animist "anti-balaka" militia led to violence that has killed thousands and displaced around 1 million people.
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