Another UK soldier and four civilians were also hurt in the blast on the Kabul-Jalabadad road.
Separately, a Nato soldier has been killed and several others wounded in a so-called "friendly fire" incident.
The deaths come amid a major offensive against the Taleban. The UK lost 14 soldiers in a plane crash on Saturday.
The soldier left wounded by the suicide attack on Monday was very seriously injured, the UK Ministry of Defence (MoD) said.
Initial reports from Afghan police said two British soldiers had been killed, but in its statement the MoD one soldier had died.
The friendly fire death happened at dawn as Nato troops battled Taleban insurgents in the Panjwayi district west of Kandahar.
The soldiers called in air support and two Nato aircraft responded, but fired cannon at their own soldiers during a strafing run.
About 2,000 Nato and Afghan soldiers are involved in Operation Medusa in southern Afghanistan.
It is the biggest military operation in southern Afghanistan since the Nato-led International Security Assistance Force (Isaf) took over the area from a US-led coalition at the end of July.
It is concentrated on the Panjwayi area, about 35km (20 miles) west of Kandahar city, which has seen months of fighting.
More than 200 Taleban fighters and four Canadian soldiers with the Nato forces were killed in the operation over the weekend, Nato said.
On Monday, police in southern Afghanistan said they had beaten off an attack by Taleban rebels on local government headquarters in the town of Garmser in Helmand province.
The town's police chief said 17 Taleban fighters had died in the attack. Three policeman were also killed during several hours of fighting.
There have been many suicide bombings in Afghanistan this year, but they are quite rare in Kabul.
A total of 124 people were killed in suicide attacks in Afghanistan up to 12 August this year, according to a statement issued by the US-led coalition forces operating in Afghanistan.
The statement said 84% of the people killed in these attacks were civilians.
Afghanistan is going through its bloodiest period since the fall of the Taleban in 2001. Hundreds of people have been killed this year as militants and troops have fought fierce battles in the south and east.
Source:BBCGüncelleme Tarihi: 20 Eylül 2018, 18:16