Mohammad Qasim, police chief for the Waghaz district in the southern Gazni province, had gone with other officers to remove a roadside bomb planted by Taliban insurgents, district governor Abdul Azim Farooqi said.
When they removed the bomb another mine concealed under it exploded, killing Qasim and two other officers. Another policeman was wounded in the blast.
In a separate incident, gunmen on a motorcycle opened fire on a car carrying Afghan army personnel in the western city of Herat, killing two officers and wounding three others, said Mohammad Nadir Fahimi, the deputy provincial police chief.
The latest attacks came a day after a bomb placed in a thermos bottle exploded at a market in northern Afghanistan, killing two men and a woman, and wounding 12 other civilians, including four women and a child, according to a local official.
Roadside bombings are a major threat to both security forces and civilians in Afghanistan. Such attacks have escalated as the Taliban have stepped up their campaign ahead of the withdrawal of US-led forces.