The blast in Zurmat district in the troubled province bordering Pakistan hit a police vehicle Saturday evening and killed all five officers on board, provincial police chief Zulmai Oryakhail told AFP.
Read: Kabul car bomb targeting foreign contractors kills 12 people
The incident and death toll was confirmed by the provincial governor's spokesperson Naqib Ahmad Attal.
No group or individual immediately claimed responsibility but both officials blamed Taliban militants for the attack.
Roadside bombs are the favourite weapon of the militants fighting to oust the Western-backed Kabul government.
Separately a bomb explosion wounded at least eight civilians in Asad Abad, the capital of Kunar province also on the border with Pakistan, provincial police chief Abdul Habib Sayedkhili told AFP.
Militants frequently target Afghan police and military, but the surge in attacks has also taken a heavy toll on civilians.
Nearly 1,600 civilians were killed and 3,329 injured in the first half of this year, according to UN figures.
Read: Kabul asks Islamabad to act against militants
NATO ended its combat mission in Afghanistan last December and pulled out the bulk of its troops, leaving the front-line fight to Afghan forces.
A 13,000-strong residual foreign force remains for training and counter-terrorism operations.
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