The explosion — one of the biggest since a truck bomb ripped through the Afghan capital's diplomatic quarter on May 31 last year — triggered chaotic scenes as terrified people fled the area where several high-profile organisations, including the European Union, have offices.
"The latest toll has reached 63 dead and 151 wounded," Baryalai Hilali, the director of the government media centre, told reporters.
The force of the blast shook windows of buildings at least two kilometres away and shattered windows within hundreds of metres of the site.
Some low-rise structures in the vicinity of the explosion also collapsed.
"The suicide bomber used an ambulance to pass through the checkpoints. He passed through the first checkpoint saying he was taking a patient to Jamuriate hospital and at the second checkpoint he was recognised and blew his explosive-laden car," interior ministry deputy spokesman Nasrat Rahimi told AFP.
Outside civilians walked through debris-covered streets carrying wounded people on their backs as others loaded several bodies at a time into ambulances and private cars to take them to medical facilities around the city.
Aminullah, whose stationery shop is a just metres from the site of the blast, said the force of the explosion shook the foundations of his building.
"The building shook. All our windows broke. The people are in shock in our market," he told AFP.
Photos shared on social media purportedly of the blast showed a huge plume of smoke rising into the sky.
A man told Tolo News he was passing the area when the explosion happened.
"I heard a big bang and I fainted," he said, outside the Emergency hospital.
"There were dozens of people who were killed and wounded. There were pools of blood."
The explosion happened in a busy part of the city where the High Peace Council, which is charged with negotiating with the Taliban, has offices.
"It targeted our checkpoint. It was really huge -- all our windows are broken," Hassina Safi, a member of High Peace Council, told AFP.
"So far we don't have any reports if any of our members are wounded or killed."
Members of the European Union's delegation in Kabul were in their "safe room" and there were no casualties, an official told AFP.
The explosion comes exactly a week after Taliban militants stormed a luxury hotel in Kabul, killing at least 22 people, the majority foreigners.
A security alert issued to foreigners this morning had warned that the Islamic State group, which has terrorised the city in recent months, was planning "to conduct aggressive attacks" on supermarkets, shops and hotels frequented by foreigners.