The assailant detonated the bomb as the convoy crossed the bridge in the morning, tossing a military vehicle into the ravine below, he said.
Major Marcin Walczak, an Isaf spokesman of the Polish army, said the international military force was aware of the incident but did not yet have any details on casualties.
Khan said the civilians who died were in a car that had pulled over nearby to wait for the convoy to pass.
Kandahar city, the capital of the province of the same name, is east of Helmand province, where thousands of US, Isaf and Afghan troops are conducting a two-week-long anti-Taliban offensive and where a roadside bomb claimed the lives of 11 civilians on Sunday.
Daud Ahmadi, the Helmand governor's spokesman, said "a civilian car struck a roadside bomb in Nawzad district" in the province's north.
Blaming the Taliban for the attack, Ahmadi said the dead included two children and two women.
Across the border, meanwhile, fighters armed with guns and rockets have blown up a tanker carrying fuel for Isaf troops stationed in Afghanistan, according to Pakistan police.
Several armed men lobbed a rocket and then opened fire on Monday on the supply convoy on the outskirts of Pakistan's northwestern city Peshawar, Imtiaz Ahmed, a senior police officer, said.
In a subsequent exchange of fire lasting up to an hour, Pakistani security forces killed a fighter, Karim Khan, another police officer, said.
Police did not immediately identify the assailants, but the Taliban and members of local group Lashkar-e-Islam regularly attack Nato supply vehicles on the main route through northwest Pakistan.