It struck near Zanbaq Square in the heavily fortified zone, with civilians said to be the main casualties.
The morning rush-hour blast created a massive crater and blew out windows and doors hundreds of metres away.
The BBC has said that Mohammed Nazir, a driver for the corporation's Afghan service, died in the explosion.
There are many other key buildings in the area, including the presidential palace and a number of embassies, including the British.
One Western diplomatic source told Agence France-Presse it was packed with more than 1,500kg of explosives.
German Foreign Minister Sigmar Gabriel said employees at the German embassy had been injured and one Afghan security guard had died.
- At least 28 dead in a huge explosion close to the Afghan defence ministry building 1 Feb 2016 - 20 killed in a suicide bomb attack at police headquarters. »