Forty people were wounded in the blast at around 8 a.m. (0330 GMT) during the morning rush-hour.
The Hezb-e-Islami insurgent group, which is allied with the Taliban, claimed responsibility for the attack on the two-vehicle convoy.
NATO's International Security Assistance Force (ISAF) said the bomber killed two of its members and four civilian contractors. It declined to give their nationalities.
But two senior officials, one Afghan and the other from ISAF, said the two ISAF soldiers and four contractors were all American.
Afghan officials said nine Afghan civilians were killed, including two children.
"Some of the dead civilians were badly burnt and cannot be recognized," Kaneshka Baktash, a spokesman for the Health Ministry, told Reuters.
Helicopters buzzed over Kabul's diplomatic area after the attack and sirens whined.
President Hamid Karzai strongly condemned the "cowardly" attack.
"Terrorists and enemies of Afghanistan's peace brutally targeted a residential area," Karzai said in a statement.
Concern about Afghanistan's prospects is growing as most foreign combat troops prepare to leave by the end of next year.
Karzai has accused neighboring Pakistan of meddling to de-stabilize his country. Analysts say Pakistan is maneuvering to limit the influence of its old rival, India, in Afghanistan.
Pakistan denies meddling and says it wants a peaceful and stable Afghanistan.
The blast caused heavy damage to buildings in the vicinity, including 10 residences.
"We were in our home drinking tea when the we heard a blast and our windows shattered, the glass wounded all of us," Zohra, a wounded girl who only gave her first name, said from a hospital bed. Her head was wrapped in a bandage.
A Hezb-e-Islami spokesman told Reuters U.S. military advisers were the targets.
"We planned this attack for over a week," the spokesman, Haroon Zarghoun, said by telephone.
Last year, in a similar attack, the group killed seven South African and Russian pilots on their way to work in Kabul.
Hezb-e-Islami, which means Islamic Party, is a radical militant group which shares some of the anti-foreigner, anti-government aims of the Taliban.
But the political wing of the group, founded by warlord and former anti-Soviet fighter Gulbuddin Hekmatyar, has been in exploratory talks with Afghan President Hamid Karzai on a peace deal to end the 12-year war.
The National Directorate of Security, Afghanistan's intelligence agency, says it thwarts a large number of attacks on the capital on a weekly basis.
The last suicide bomb attack in Kabul was in March, when a man blew himself up at a Defense Ministry gate, killing nine Afghans, during a visit by U.S. Defense Secretary Chuck Hagel.
(Additional reporting by Hamid Shalizi and Mirwais Harooni, writing by Amie Ferris-Rotman, Editing by Robert Birsel)