Despite tight security, the suicide bomber managed to drive into the city in a car laden with explosives.
The convoy was attacked on the Darulaman road, one of the main roads in the city.
A spokesman for the Nato-led international peacekeeping force Isaf confirmed that six of its soldiers had been killed. Apart from the five US soldiers, one Canadian is believed to have been killed.
Nato chief Anders Fogh Rasmussen "strongly" condemned the attack, but said the alliance remained "committed to its mission to protect the Afghan people and to strengthen Afghanistan's ability to resist terrorism".
Five military vehicles were damaged and more than a dozen civilian vehicles, including a bus, were also caught in the blast.
The BBC's Mark Dummett in Kabul says that, as is often the case in such attacks, Afghan civilians seem to have borne the brunt of the explosion.
Eyewitness Obiadullah Saddiqyar was on his way into work when the bomb detonated. He described the scene as "totally chaotic".
He told the BBC: "I witnessed the bomb this morning at around 0815 [0345 GMT]. I saw many people dead and many injured who were taken to hospital.
"Among the dead there were lots of women and girls - I heard later that they were students going to university. I also saw one of my colleagues full of blood in the back of a police car, also being taken to hospital.
"This situation really made me cry for the bloodshed and the innocent people who were killed and injured."
Afghan police have set up extra checkpoints throughout the city this year following a series of attacks by gunmen and bombers on government offices and hotels, our correspondent says.
They say they have arrested several men planning suicide attacks but it is impossible to stop and search every car, so these attacks seem certain to continue, he says.
Major offensive
Afghan President Hamid Karzai described the attack as "heartbreaking".
"We are condemning the attack in the strongest terms. I hope Afghanistan will soon get out of this suffering, God willing," he said at a news conference broadcast on national television.
President Karzai has recently returned from a trip to Washington where he hoped to gather support for his policy of reconciliation with certain elements of the Taliban.
Afghan officials are also preparing for a jirga (English: grand council) of tribal leaders, during which ways to promote peace in Afghanistan will be discussed.
Meanwhile a military offensive in the southern province of Kandahar, a key Taliban stronghold, is being planned.
Earlier this year Nato and Afghan forces launched a major offensive against militants entrenched in neighbouring Helmand province and security forces are still engaged in operations around Helmand.
Nato and the US have deployed thousands of extra troops in Afghanistan, where numbers are expected to peak at 150,000 in August under a strategy designed to bring a swift end to the long-running insurgency.