The explosion on Wednesday ripped through a car carrying General Salim Khan on a road in front of a base of the US military's Provincial Reconstruction Team in Kandahar city, they said.
Khan blamed the attack on remnants of the Taliban militia that were ousted by US -led forces in late 2001.
"The Taliban did it," he said from a hospital where he was treated for face and hand injuries.
However, nobody has claimed responsibility for the attack, reported our correspondent.
The Taliban and their al-Qaida allies have declared a jihad on foreign and Afghan government troops and aid organisations. Since August last year, more than 600 people have been killed in violence blamed mainly on the resurgent Taliban.
Wednesday's blast is the first in several months in Kandahar, a former Taliban stronghold, and follows sporadic rocket attacks over the past three nights around Kandahar province which caused minor damage, but no casualties.
It also comes two days after the Taliban said they killed a provincial security chief and his two bodyguards in neighbouring Uruzgan province and threatened to step up attacks against the government and the 15,500 US-led foreign troops in the country.
Khan said the bomb appeared to have been planted on a speed bump and detonated by remote control.
Provincial Reconstruction Teams usually consist of about 60 soldiers involved in military and civilian projects.
Dozens of civilians were killed and wounded in Kandahar city in a bomb blast in January that authorities also blamed on Taliban fighters.
Unrest in southern and eastern Afghanistan prompted President Hamid Karzai's US-backed government to postpone the country's first-ever presidential and parliamentary elections from June to September.