Police said the truck then slammed into a home, but no one inside was harmed.
The accident occurred in the same area of Kabul where another crash last month involving U.S. forces sparked deadly riots.
There was no immediate sign of unrest after today's accident.
Police and U.S. troops quickly cordoned off the area, while dozens of people from the neighborhood stood and watched.
Five civilians were killed in the May 29 crash, when a U.S. military truck plowed into a line of cars.