Khairudin Shuhja, district police chief, said the convoy was carrying the police chief of the Gereshk district.
Guards opened fire on the attacker and wounded him, Shuhja said, but failed to stop him from detonating his explosives.
Meanwhile, five security officers were killed and seven others injured in an attack on a police post in the eastern Kunar province.
That attack was carried out by Taliban fighters, Abdul Jalal Jalal, provincial police chief, said.
Three officers were also killed in the northwestern Badghis province when their patrol hit a mine, General Khalil Andarabi, a regional police officer, said.
More than 900 policemen were among 8,000 people killed last year in violence linked to the Taliban-led insurgency against the government in Kabul, officials said.