Afghan intelligence officials said four Filipinos and two Afghans were confirmed among the dead when a lone gunman opened fire, threw at least one grenade and then detonated his explosive harness.
Women and a child were among those killed.
The Taliban immediately took responsibility in a text message claiming it had targeted the chief of the Blackwater security contracting firm.
The 2.30pm (10am GMT) blast struck Finest Supermarket in the relatively secure central Wazir Akbar Khan district which is popular with embassies.
The shop is across the road from the fortified British embassy compound and is frequented by expats for its range of Western groceries. Witnesses said the shop was full of foreigners on what is the Afghan weekend.
Mehrab Gol, who sells mobile phone cards outside the shop, said: "The suicide bomber fired first and then threw a grenade and then he blew himself up.
"Then there was chaos inside and people were running away. There were many wounded but there was nobody there to carry them away." Afghan police and soldiers cordoned off the area and Nato forensic experts were seen entering the supermarket.
The assault was the most serious targeting civilians inside Kabul for a year.
Hamid Karzai said the "enemies of Afghanistan are so desperate that they are now killing civilians, including women, inside a food market."
He said such attacks were against Islam and had no place in Afghan culture.
The American embassy said: "Numerous innocent Afghan and international civilians were killed and wounded in this senseless act.
"By attacking a peaceful place of commerce, insurgents have once again demonstrated their lack of respect for the safety of the Afghan people."
