Zabiullah Mujahid, a Taliban spokesman, said that the target had been the US embassy but the bomber had exploded his device at the checkpoint as he was not able to reach it.
"The suicide car bomber exploded near the Isaf headquarters and killed several foreign troops," Mujahid said.
It was not immediately possibly to confirm the identities of those killed in the attack.
But Al Jazeera's James Bays, reporting from Kabul, said Isaf officials confirmed that some of their military personnel were among the injured.
"This bomb has taken place in one of the areas that should be one of the most secure areas of the Afghan capital," he said.
"It is a scene of devastation. It is clear the bomber managed to make it through the outer layer of security, which is provided by the Afghan security forces, and right outside the main gate of the military base."
The blast shattered windows in the area and shook buildings in the Wazir Akbar Khan district, home to most of the major foreignembassies and organisations in the capital.
Children, who gather outside the gate of the compound to sell items to Westerners, were reportedly among the injured.
The attack comes just days before Afghans head to the polls for presidential elections and provincial council elections.
Hamid Karzai, the Afghan president, condemned the attack, but said it would not stop Afghans from voting on Thursday.
"The enemies of Afghanistan try to create fear among people in this election period but people still realise the importance of going to ballot boxes to cast their votes," Reuters reported, citing a statement from the presidential palace.
The Taliban leadership has called the election an American invention, and has threatened to disrupt voting across the country.
According to the United Nations, violence and intimidation have already disrupted planning and campaigning in the country's south, and could prevent many Afghans from casting their ballots.
Election officials have said fears of violence could prevent hundreds of polling stations from opening and that voting was unlikely in nine of 365 districts.
Also in Kabul on Saturday, four civilians were killed when their vehicle was hit by a roadside bomb and in Paktia province four people were wounded by a suspected suicide bomber.