A deputy police chief in the southern province of Kandahar has also been shot dead when leaving a barber's shop, police said.
General Mohammad Daud Saleh was shot by men on a motorbike in Kandahar city, General Ismatuallh Alizai, the provincial police chief, said.
He is the most senior policeman to be assassinated in the province.
Alizai blamed the attack on the "enemies of the country", a term Afghan officials use to mean Taliban members who have been joined by other fighters, including from al-Qaeda.
On Saturday, Nato forces began joint patrols in the streets of the Sangin region in southern Afghanistan, after forcing out the Taliban.
The coalition forces said they recovered the territory, situated in Helmand province, following clashes which have lasted for weeks.
The police are on the frontline of the conflict with the Taliban, with more than 200 officers killed this year, according to a news agency estimate.
On Friday, five police officers were killed when a group of Taliban fighters attacked a district office in the town of Ghorak, Kandahar, Alizai said.
A dozen Taliban members were also killed, he said.
Elsewhere in Kandahar, Taliban fighters ambushed a police vehicle with rocket-propelled grenades early on Saturday, Alizai said.
"Five police were killed and four more wounded," he said. A spokesman for the Taliban confirmed that his group was behind both attacks.
In another attack on police, a remote-controlled bomb killed a policeman and wounded three others in the province of Laghman, immediately east of Kabul, a governor's spokesman said on Friday.
The Taliban rose from Kandahar in the early 1990s to take control of government by 1996. They were removed in 2001 by a US-led coalition that remains in the country today.