The attack underscores spiralling insecurity in Afghanistan, where the military is struggling to beat back the insurgents.
"It is with great sadness that the BBC can confirm the death of BBC Afghan driver Mohammed Nazir following the vehicle bomb in Kabul earlier today, as he was driving journalist colleagues to the office," the BBC World Service said in a statement.
"Four BBC journalists were also injured and were treated in hospital. Their injuries are not thought to be life threatening," the statement said.
"Mohammed Nazir worked as a driver for the BBC Afghan Service for more than four years and was a popular colleague. He was in his late thirties and he leaves a young family," it said.
"This is a devastating loss to the BBC and to Mohammed Nazir's friends and family. We are doing all we can to support them and the rest of the team in Kabul."
The truck bomb killed 80 people and wounded hundreds more.
The attack underscores spiralling insecurity in Afghanistan, where a military beset by soaring casualties and desertions is struggling to beat back the insurgents.
More than a third of the country is outside government control.