The gunmen are believed to have been shot dead by security forces when they arrived at the scene.
The IMF said its resident representative in Afghanistan, Lebanese national Wabel Abdallah, 60, died in the bombing and shooting by Taliban suicide attackers on the popular restaurant.
"This is tragic news, and we at the fund are all devastated," IMF Managing Director Christine Lagarde said in a statement.
"Our hearts go out to Wabel's family and friends, as well as the other victims of this attack."
Abdallah had been the IMF's resident representative in the country since June 2008, and had worked with the Fund since 1993, especially in its Middle East activities.
The Taliban confirmed it had carried out the attack on La Taverna du Liban, a restaurant popula with foreigners and wealthy Afghans alike.
The blast happened at a heavily secured restaurant in the Afghan capital
It described the building as a “foreign hotel” and said the blast targeted “high-ranking German officials” it described as “foreign invaders”.
The German foreign ministry said it was looking into the claims, while Ari Gaitanis, a spokesman for the UN said at least four of its employees remained unaccounted for.
Kebab cook Abdul Majid, who suffered leg fractures in the blast said, “I was sitting with my friends in the kitchen when an explosion happened and smoked filled the kitchen.
“A man came inside shouting and he started shooting. One of my colleagues was shot and fell down. I ran to the roof and threw myself to the neighbouring property.”
The restaurant's chef, Abdul Majid, was among those injured - AFP PHOTO/STRINGER
Like many places that are popular with diplomats, aid workers and businessmen in Afghanistan, the restaurant has no signs indicating its location and is heavily secured.
It has no windows, bags of dirt are piled up outside to act as blast walls and guests are searched before entering the premises.
