Police say it was a suicide attack on a foreign military convoy which was travelling through the area.
A health ministry official said nine Afghans were among the dead.
A senior Nato official confirmed that three American contractors had been killed in the attack in the Macrorayan district.
No group has said it carried out the attack, although in recent months Kabul has been regularly targeted by the Taliban in a series of bombings.
The explosion took place not far from Kabul airport and the presidential palace. Witnesses said that children were among the injured and some foreigners were trapped in a destroyed vehicle.
An interior ministry spokesman quoted by the AP news agency said the blast destroyed more than a dozen civilian vehicles.
The bombing, close to a civilian hospital, is the latest in a series of recent deadly attacks following the announcement of a new Taliban leader.
Earlier this month, a Taliban suicide bomber attacked a checkpoint near the entrance to the international airport in Kabul, killing five people.
Before that, there were three deadly attacks in the city - on a police academy, a Nato base and an Afghan army base that killed at least 50 people.
The Taliban has stepped up its campaign of violence in recent months, taking advantage of the warmer weather of spring and summer. It has made some military gains, especially in northern Afghanistan.

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Ainslie, 35, admits it would have been "difficult to top" the feeling of winning at his home Olympics and is keen to move on with new challenges.
"It was a tough decision," Ainslie told BBC Sport.
"I've had a fantastic Olympic career but I want to make it clear that the focus is now on the Americas Cup."
Ainslie won a silver medal at Atlanta 1996, with golds in Sydney, Athens, Beijing and London. He has won more medals than any other sailor, ahead of Denmark's Paul Elvstrom, who has four golds.
He is fourth in Britain's all-time individual medallist's list, behind Sir Chris Hoy (cycling; six gold, one silver), Sir Steve Redgrave (rowing; five gold, one bronze) and Bradley Wiggins (cycling; four gold, one silver, two bronze).
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Ainslie added: "I considered all of the factors - my fitness and the issues with my back, the venue for the next Olympics and the type of boats, but what it really came down to was this opportunity with the Americas Cup."
The sailor envisages skippering his Ben Ainslie Racing AC45 catamaran to glory in the historic competition will be one of the "biggest tests" of his career.
"It's always been a dream of mine since I was a kid to be part of a winning Americas Cup team and ultimately I want to try and bring it back to the UK where it all started in 1851."
Ainslie, who won his first Games medal - a silver in the Laser fleet - at Atlanta 1996, says he may have extended his Olympic career into a twentieth year had the International Sailing Federation [ISAF] reversed their decision to axe the Star class from Rio 2016.
"There was a possibility that it may have been reinstated, but that didn't happen," reflected the four-time World Sailor of the Year Award winner.
"There would have been no guarantees I would have made it to the Olympics going up against 2008 gold medallists Iain [Percy] and Andrew [Simpson], but certainly it was an option to go into that class."
Ainslie ranked his success in London as his greatest personal Olympic moment, but that attaining a first gold at the Sydney 2000 Games was a close second.
"It meant a huge amount to me to reverse the silver medal from 1996 and it gave me a huge amount of confidence that I could go on and achieve more," stated Ainslie who switched from the Laser to the Finn dinghy for Athens 2004.
"I am proud of what I achieved [in the Olympics] but I think this decision [to retire from dinghy sailing] really helps to make it clear what the goal is and the intensions are.
"Hopefully now we can go ahead and get the support to make that [Americas Cup success] happen."
An explosion has rocked the diplomatic area of the Afghan capital, Kabul, police have said, with at least 12 people killed and 60 injured.
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British sailor Ben Ainslie will not bid for a fifth Olympic gold medal at the 2016 Rio Games and will instead focus on his Americas Cup campaign.