The explosion killed 21 civilians and four policemen in Logar province, south of Kabul, and also demolished nearby dairy shops, Interior Ministry spokesman Zemerai Bashary said.
Authorities suspect the truck may have been heading into Kabul with the explosives, but that it overturned on the main road between Logar province and the capital late Wednesday, provincial police chief Mustafa Khan said.
After police arrived to clear the road, militants apparently decided to blow up the truck where it overturned, Khan said, adding that authorities believe the explosives were mingled with timber in the back of the truck and that they were remotely detonated.
The power of the blast sent truck pieces more than a mile away, another police official said.
The blast took place in Mohammad Agha district, close to shops that collect milk from farmers. At least six of those killed were students from a nearby primary boys school, the second police official in Logar said. He spoke on condition of anonymity because he was not authorized to speak to the media.
A senior police official told CBS News' Fazul Rahim that no foreign soldiers were involved in the attack Thursday. The official said initial reports of possible involvement by foreign troops may have been due to the fact that there were some coalition forces nearby and they helped police cordon off the area after the explosion.
The blast happened as thousands of U.S. Marines in southern Afghanistan are involved in the biggest American military offensive in country since the ouster of the Taliban from power in 2001.
At left, click to watch video released by the Pentagon of Marines from Fox Company, 2nd Battalion, participating in "Operation Strike of the Sword" in Kandahar province.
The top Marine in the U.S.-led offensive said Wednesday that heto help clear the Taliban from the nation's poppy-growing region.
Marines Brig. General Larry Nicholson told Pentagon reporters Wednesday that he'd like more U.S. troops too, but that they're not necessary.
Nicholson said the greatest danger to the 4,000 U.S. troops leading the operation that began a week ago in Helmand province is unrelenting heat he described as "hot as fire."