"The explosion happened 20 metres from the vehicles of the IEC employees", Kabul police spokesman Basir Mujahid told AFP.
"People are determined to take part in the election because they want to show the Taliban that terror can not stop the Afghans from deciding their future", Dawa Khan Menapal, an independent candidate, said before the voting in Kandahar.
Voting in the region was pushed back due to a Taliban attack on the eve of the elections, killing provincial police chief Gen. Abdul Raziq, intelligence chief Mumin Hussainkhil, and a journalist.
The polls open Saturday in a southern province of Afghanistan, where the legislative elections, held last week in the country, had been postponed after the assassination by the taliban, a powerful chief of the local police.
On Saturday voters in Kandahar - the southern birthplace of the Taliban and a province notorious for ballot stuffing - went to the polls.
Streets in the city were quieter than usual at the beginning of the Afghan working week, after authorities restricted the use of cars and motorbikes during voting hours.
On election day, the Taliban had carried out around 200 attacks, which left at least 36 dead and 126 wounded.
IEC figures show roughly 4.2 million out of the almost nine million people registered to vote actually cast a ballot. More than 2,500 candidates are competing for the 250 seats in the lower house.
The Taliban claimed that attack and said they also targeted Washington's top commander in Afghanistan, Gen. Scott Miller, who was unhurt.
"Most of the complaints are against the voter's registration lists, the second complaints were against the observers - that some observers were encouraging people to vote for their favorite candidates - but the main challenge was the late opening of the stations and the lack of materials", said Karimullah Stanikzai head of IECC regional office.
This year's elections have become the first parliamentary election in Afghanistan since 2010.
Preliminary results of nationwide voting for Afghanistan's 249-seat Parliament are not expected before mid-November.