The vehicle was hit in the Dilaram district of Farah province, said defence ministry spokesman General Zahir Azimi.
Mohammad Sarwar Sebat, the governor of neighbouring Nimroz province, told AFP the soldiers were transporting ammunition to Farah from their base in Nimroz when the blast struck them.
The governor said the remote-controlled bomb killed five soldiers and three officers.
No one has claimed responsibility for the attack, but roadside bombs have been the weapon of choice for Taliban insurgents in their 12-year battle to topple the US-backed central government.
More than 50,000 NATO combat troops still in Afghanistan are due to leave by the end of the year, and will leave the huge task of providing security to local forces.