Police chief Khan Muhammad Khan said on Wednesday that there were likely to be many more casualties and that the explosion might have been caused by a time bomb.
The explosion occurred shortly before 9am (0430 GMT) at a base used by an Afghan militia corps he had previously commanded.
The blast comes just hours after provincial authorities said they had caught a close associate of Taliban leader Mulla Muhammad Umar, just outside Kandahar.
Eight other suspected Taliban fighters were arrested at the same time, and several remote control bombs, time bombs, different explosive devices and radios were also seized.
Meanwhile, a Turkish engineer was kidnapped in eastern Afghanistan on Tuesday along with his Afghan driver and interpreter, police said.
The engineer, working on a road-building project between the southeast city of Jalalabad and Kunar to the east, was snatched at around 8am, according to Kunar deputy police chief Arif Nizami.
A small Islamist group operating in a heavily forested mountainous area close to the border with Pakistan was suspected of being behind the abduction.
Nizami said the group had about 20 members and was led by a commander called Hazrat-e-Umar, who had links in the past with the larger the Hizb-i-Islami movement led by renegade former prime minister Gulb al-Din Hekmatyar, now an ally of the Taliban.
The kidnapping took place near the village of Spin Jamahat, about just south of Asadabad and 175km northeast of Kabul.
There have been several isolated cases of kidnappings in the past year, notably involving Turkish and Indian road construction workers.