The suspect had confessed to carrying the small weapon for someone else in the eastern district of Batticaloa, in return for cash, it added.
The UN said in a statement that the aid worker was travelling in a private vehicle outside his working hours at the time of his arrest.
"The matter is currently under police investigation while the UN is fully co-operating with the authorities," the UN said in a release.
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Government officials frequently accuse international aid groups of pro-rebel leanings.
Last year, the foreign ministry asked the United Nations Children's Fund to withdraw some of its foreign staff for having taken part in a peaceful demonstration against the killing of local Red Cross workers.
UN officials have said that Sri Lanka is among the most dangerous places for