The incident occurred on Friday morning 40 km south of Kabul on the road to Kandahar. The International Security and Assistance Force said the bus driver did not heed signals to slow down, warning gestures or shots in the air, so the soldiers were forced to fire on the vehicle.
Several other passengers were wounded and were given emergency medical assistance, the press service said, adding that some were flown to a military hospital.
Also on Friday, four British soldiers died in two separate explosions in southern Afghanistan, Britain's Ministry of Defense said on Friday.
One of the Royal Marines was killed in an explosion while on a routine patrol in the Sangin area of Helmand province, while the other three were involved in operations against local militants south of Sangin.
Meanwhile, the bodies of two Afghan policemen captured earlier this week by Taliban forces in the northern Kunduz province were found on Saturday, a provincial security spokesman said.
The bodies were discovered on information from the insurgents, who staged an ambush when the Interior Ministry troops came to recover their colleagues. There were no casualties among the Afghan police involved in the encounter.
The whereabouts of the third captured policeman is unknown.
