The attack killed one service member, Major Marcin Walczak of the Polish army, a spokesman for the Nato-led International Security Assistance Force (Isaf), said without providing the nationality or any other details.
The Afghan interior ministry confirmed the four civilian deaths in a statement.
The assailant had waited in a taxi near a bridge between the airport and Kandahar city that Isaf troops regularly check for explosives, Inhamullah Khan, an Afghan army official at the bombing site, said.
The attacker detonated the bomb as the convoy crossed the bridge in the morning, hurling a military vehicle into the ravine below, he said.
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 blew 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.