The employee, who was working with peacekeepers, was snatched from his residence in the city of Fasher.
Security Council envoys had arrived in Fasher to raise concerns about an upsurge in violence in Darfur.
Earlier, Sudanese armed forces, long accused of atrocities in Darfur, launched renewed attacks on rebels.
The government forces said they had taken a key stretch of road from the rebel Sudan Liberation Army, about 100 miles (160km) away from Fasher.
The rebels said aircraft had bombed villages full of civilians - allegations that the government denied.
Later on Thursday, the joint UN-African Union peacekeeping force, Unamid, told journalists that that one of their workers had been snatched.
"Armed men entered the residence of four civilian staff members in downtown El Fasher," said spokesman Kemal Saiki.
"They tied up two of them and made away with the other two in a vehicle. One man escaped and the other is still missing."
He said the kidnap was unrelated to the visit of the Security Council diplomats. The nationality of the kidnapped person has not been disclosed.
Ambassadors and top diplomats from the 15 nations on the UN Security Council are on a four-day mission to Sudan.
Q&A: Darfur conflict
They were in talks in Khartoum to check the troubled preparations for a secession vote for the south, due to take place in January, and also visited Juba before they moved on to Fasher.
Heavily armed peacekeepers greeted them at the airport, along with hundreds of protesters, voicing their support for Sudanese President Omar al-Bashir.
The UN delegation had refused to meet Mr Bashir, who is wanted by the International Criminal Court (ICC) for alleged war crimes committed in Darfur - charges he strongly denies.
The BBC's James Copnall, in Khartoum, says several foreigners have been kidnapped in Darfur since the warrant was issued.
Our correspondent says most of the abductions appear to be motivated by money rather than politics, but he says the timing of this incident will be deeply worrying for Unamid.
The UN estimates the six-year conflict in Darfur has cost the lives of 300,000 people and driven a further 2.7m from their homes.
The government puts the death toll at 10,000 and has said the problems in Darfur have been exaggerated for political reasons.
A UN employee has been kidnapped in Sudan's Darfur region, officials say, hours after a Security Council delegation arrived in the area.