The protesters had gathered in support of a parliamentary candidate who electoral officials had disqualified over his suspected links with illegal armed groups. Eight people were also wounded.
No group has claimed responsibility for the attack.
Burqa-clad suicide bombers kill at least 29 inside Afghan a mosque
Attaullah Khogyani, a spokesperson for the provincial governor, said the explosion happened when supporters of the disqualified candidate were trying to shut down the election commission office.
"We had requested the protesters to stop their demonstrations because they could be targeted by militants but they rejected our security message," he said.
A suicide bomber blew himself up outside an Afghan election office in the capital, Kabul, earlier this month when protesters gathered to challenge the commission's decision to disqualify 35 candidates from contesting upcoming parliamentary polls.
Suicide attack kills three NATO soldiers in Afghanistan
One police official was killed in that attack. A ban on dozens of Afghan strongmen and lawmakers from running for parliament because of suspected links to illegal armed groups has spurred threats and protests to disrupt a general election that is already at risk from worsening security.
The Taliban have warned people not to vote in the October polls and dozens of people have been killed in militant attacks on voter registration centres. Supporters of disqualified candidates have held sit-in protests outside a number of election commission offices around Afghanistan over the past two weeks. Security forces launched a drive to evict them on Saturday.
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