The blast came shortly after 8:00 am (0900 IST), not far from the Iranian embassy. Police said the dead included a Turkish national and an Afghan passer-by.
Kabul police spokesman Hashmat Stanikzai gave details of the attack and death toll, saying the bomber was driving a Toyota Corolla when he targeted the Turkish vehicle.
Abdul Rahman Rahimi, Kabul police chief, confirmed the death toll in the blast, which the Taliban claimed.
The area was cordoned off after the blast, which left debris strewn in the road and nearby blast walls spattered with blood.
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Eyewitness Mohammad Yousuf, 17, described the moment the blast happened.
"The suicide bomber was in a Toyota sedan, he detonated himself causing a big bang, soon after the explosion everywhere were black smoke," he told AFP.
It is the first major attack in Kabul's heavily-secured centre since early January, when a suicide bomber hit a European Union police vehicle, killing a passer by.
NATO ended its combat mission in late December, leaving a residual force to carry on a training and support mission to Afghanistan's 350,000 security forces, who now lead the fight against the Taliban.
There have been growing hopes in recent weeks of talks between Kabul and the Taliban aimed at moving towards reconciliation after more than a decade of war.
Afghanistan's chief executive Abdullah Abdullah said on Monday that dialogue with the Taliban could begin soon and last week several militant commanders said preliminary meetings in Qatar were on the cards.
There have been several attempts at starting dialogue in recent years between the Taliban, Kabul and the United States - the Afghan government's chief supporter - but with little success.