The Wazir Akbar Khan district is home to most of the capital's foreign embassies as well as several major government institutions, including the Presidential Palace.
The bomb, concealed in a water delivery truck, detonated at 8:22 a.m.
CGTN's Catherine James reports from the blast site.
NATO's Resolute Support Mission said that Afghan security forces had prevented the truck carrying explosives from entering the Green Zone.
Dozens of damaged cars choked the roads as wounded survivors sought safety.
"That this attack would occur during the holy month of Ramadan underscores the senseless and barbaric nature of this attack", a White House spokesman said.
Prime Minister Justin Trudeau tweeted his condemnation of the attack.
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The sound of the bomb, which went off near Kabul's busy Zanbaq Square, reverberated across the Afghan capital, with residents comparing it to an natural disaster.
Relatives of Afghan victims mourn outside a hospital after a blast in Kabul, Afghanistan, on Wed., May 31, 2017.
BBC World Service director Francesca Unsworth says Mohammed Nazir, who had worked for the BBC Afghan Service for four years, was killed as he was driving colleagues to work. He suggested that the German embassy might not have been the target of the blast.
Pictures showed the embassy building with its windows ripped out, Reuters reported.
There were 11 US citizens - all contract personnel - injured in the blast and one Afghan local guard was reported missing, Fox news reported a senior USA official as saying.
Despite the massive security apparatus surrounding the German embassy, the blast wave of the truck bomb managed to inflict extensive damage. "All the targets were hit", a Russian military statement said.
Northeastern University professor Max Abrahms, who researches the strategic effectiveness of terrorism, suggested the attack was created to encourage a US exit from Afghanistan.
"There are a large number of casualties, but I don't know, how many people are killed or wounded", said an eyewitness at the site, Gul Rahim. Germany won't carry out flights deporting rejected asylum seekers to Afghanistan in the next few days, a German official confirmed, but stressed the underlying policy remained. The European nation has drawn criticism for sending back Afghans to an increasingly risky country.
President Ashraf Ghani made a televised address late on Wednesday, calling for national unity in the face of the attack, which his National Directorate for Security blamed on the Taliban-affiliated Haqqani network, but he faces an increasingly angry public. The death number is probably higher than 80.