Bodies littered the scene and a towering plume of smoke rose from the area, which houses foreign embassies, after the blast blew out the windows in several missions and residences hundreds of metres away.
Witnesses described dozens of cars choking the roads as wounded survivors and panicked schoolgirls sought safety. Men and women struggled to get through security checkpoints to search for loved ones.
It was not immediately clear what the target was. But the attack underscores spiralling insecurity in Afghanistan, where a military beset by soaring casualties and desertions is struggling to beat back the insurgents. Over a third of the country is outside government control.
The interior ministry said in a statement that at least 64 people had been killed and 320 wounded, including women and children.
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A suicide bomber detonated an explosives-packed vehicle in Zanbaq Square around 08:30 am, the ministry said in a statement. "More than 50 vehicles were either destroyed or damaged."
Authorities warned the toll could yet rise. "They are still bringing bodies and wounded people to hospitals," senior health ministry spokesman Ismael Kawoosi told AFP.
There was no immediate claim of responsibility, but the attack came as the resurgent Taliban step up their annual "spring offensive".
The Islamic State group has also claimed responsibility for several recent bombings in the Afghan capital, including a powerful blast targeting an armoured NATO convoy that killed at least eight people and wounded 28 on May 3.
France also reported damage to its own embassy and the German one. There was no information on possible casualties.
Afghan troops are backed by US and NATO forces, and the Pentagon has reportedly asked the White House to send thousands more troops to the country to break the deadlock in the fight against the Taliban.
The blast was the latest in a long line of attacks in Kabul. The province surrounding the capital had the highest number of casualties in the first three months of 2017 due to multiple attacks in the city, with civilians bearing the brunt of the violence.