At least nine people, including three members of the Nato-led peacekeeping force, were injured in the attack on Saturday.
A purported Taliban fighter with grenades strapped to his body detonated several of them on a Kabul shopping street popular with foreigners, initially killing himself and wounding seven others, including three Nato soldiers from Iceland.
A US embassy spokeswoman confirmed an American citizen had died after the attack.
In the US, relatives of Jamie Michalsky, a 23-year-old translator, said she had died of injuries she had suffered in the blast.
An 11-year-old girl, a bookseller on the popular Chicken Street, was among the injured, but died of her wounds at a local hospital several hours later.
Three of six grenades strapped
Kabul police chief General Baba Jan said the attacker on Saturday had six hand grenades strapped to his body, three of which failed to detonate.
“One person was killed who is believed to have been the attacker,” said Lieutenant Colonel Patrick Poulain, spokesman at the headquarters of the Nato-led International Security Assistance Force (ISAF) in the Afghan capital.
The bloody corpse of the attacker lay on the pavement, near a damaged ISAF vehicle, witnesses said.
The three ISAF soldiers were reported to be members of the Iceland contingent.
Chicken Street is a well-known haunt for foreigners shopping for carpets, jewellery and antiques.
Poulain said seven people were wounded in the blast.
The 18,000 US soldiers are often
One of the ISAF troops was in a serious condition, while the
other two were only slightly hurt.
The Afghan capital has escaped major attack for the past two months as security forces stepped up operations to stop Taliban fighters and their allies disrupting a landmark presidential election on 9 October.
In late August, a car bomb killed at least eight people,
including three Americans working for a private security company contracted by the US Department of State to provide bodyguards to President Hamid Karzai and help train Afghan police.
ISAF has about 9000 troops in Afghanistan acting as peacekeepers in Kabul and nine northern provinces, while
US-led forces numbering in excess of 18,000 are said to be scouring the south and south-east for Taliban and foreign al-Qaida fighters.