Lt Damien E Horvath, a military spokesman, could not say how many casualties there were or provide their nationalities.
The NATO mission, known as Resolute Support, “can confirm that a NATO convoy was attacked in Kandahar. The attack did cause casualties,” he said.
Kandahar police spokesman Zia Durrani also confirmed the attack and the area on the edge Kandahar was quickly cordoned off.
No one immediately claimed responsibility for the bombing.
Eyewitness Ghulam Ali, who runs a mechanics shop near the attack site, said the intensity of the blast knocked him out.
When he came to he saw one military vehicle ablaze on the road.
He stepped out of his shop but a sudden burst of gunfire drove him back inside.
He heard helicopters arriving and saw soldiers being taken away from the scene but could not determine the extent of their injuries.
Shah Agha Popal, who runs a vehicle parts shop also nearby, said he also saw soldiers being taken away by two helicopters.
“But I couldn’t tell if they were wounded or if they were dead,” he said.
The combined US and NATO troop contingent currently in Afghanistan is about 13,500.
The Trump administration is deciding whether to send about 4,000 or more US soldiers to Afghanistan in an attempt to stem Taliban gains.
The attack came as Afghan authorities in western Herat province tightened security ahead of a mass funeral for the victims there of an attack the previous evening that killed 29.
A suicide attacker opened fire inside a mosque packed with worshippers at evening prayers, before detonating his explosives. A second explosion came 10 minutes later.
No one has claimed responsibility for that attack either, but it came a day after the Islamic State group warned it would strike Shiites. The Sunni militant group considers Shiite Muslims as apostates.
Herat provincial spokesman Jilani Farhad said that to reduce the possibility of more attacks, a planned Shiite protest against the attack was to be held just before the burial on Wednesday afternoon, rather than at a separate time and location.
Along with the 29 killed, 64 people were wounded, 10 of them critically.