The offices of the European Union and the High Peace Council are also nearby, along with a number of foreign embassies and the police headquarters.
An AFP reporter said he saw "lots of dead and wounded" people in a nearby hospital.
Wahid Majroh, a public health ministry spokesman, confirmed to Xinhua that 79 injured had been shifted to Kabul hospitals after the deadly incident.
On Dec. 28 a suicide bomber and other explosions at a Shiite cultural center in Kabul killed at least 41 people in an attack claimed by the Islamic State group that may have been aimed at a pro-Iran news outlet based in the building.
Thick, dark smoke could be seen rising from the site of the explosion near the old Interior Ministry building.
The force of the blast shook windows of buildings at least two kilometres (more than a mile) away and shattered windows within hundreds of metres of the site.
In chaotic scenes at the Jamuriate hospital, which is the nearest medical facility to the blast, overwhelmed doctors and nurses rushed to treat dozens of wounded lying in the corridors.
A security alert issued to foreigners on Saturday morning warned that ISIL, which has terrorised the Afghan capital in recent months, was planning "to conduct aggressive attacks" on supermarkets, shops and hotels frequented by foreigners.
People helped walking-wounded away as ambulances with sirens wailing inched their way through the traffic-clogged streets of the city centre.
Wounded people are assisted at the site of an explosion in downtown Kabul, Afghanistan, Saturday, Jan. 27, 2018.
"I strongly condemn the suicide vehicle bomb attack in the Afghan Capital". Attahullah Khogyani, spokesman for the provincial governor said a group of gunmen stormed the office of the non-governmental organization, Save the Children.