The charity later said that it would pull nearly all of its personnel out of Darfur following the kidnapping, with only those staff working on securing the release of their kidnapped colleagues would stay.
The Belgian foreign ministry confirmed the kidnapping had taken place and said that none of its nationals were involved in the incident.
Ali Sadig, a spokesman for Sudan's foreign ministry, told Al Jazeera: "What we know right now is that there is some sort of negotiation between the local authorities and the hostage takers.
"We do not know how far those negotiations have gone but people are doing their best to ensure the safety and secure the release of the three foreigners."
The attack on the Belgian MSF branch came days after the French and Dutch contingents of the aid organisation were kicked out of Darfur.
They were among 13 aid groups ordered to leave Sudan after the International Criminal Court (ICC) issued an arrest warrant against Omar al-Bashir, Sudan's president, for alleged war crimes in Darfur.
Khartoum accuses the expelled aid groups of co-operating with the ICC, which says that al-Bashir led a violent campaign in Darfur over the past six years.
The United Nations says that more than 180 foreign aid workers have left Sudan since the order by Khartoum to expel the aid groups.
The World Food Programme (WFP) says four of its partner relief agencies expelled from Darfur were looking after 35 per cent of food distribution to the region.
Barack Obama, the US president, said on Tuesday that the expulsions were unacceptable.
"We have a potential crisis of even greater dimensions than we already saw," Obama said.
The US embassy in Khartoum has permitted non-essential staff to leave Sudan and has boosted security measures after getting information of "terrorist threats" aimed at Western interests in the country.
About 300,000 people have died in Darfur from the combined results of war, famine and disease over the course of the last six years, the UN has said. At least 2.7 million people have been displaced, it says.
The conflict in Darfur erupted after ethnic fighters rebelled against the Arab-dominated government.