"The explosion happened 20 metres from the vehicles of the IEC employees", Kabul police spokesman Basir Mujahid was quoted as saying by AFP.
"The wounded were taken to hospital and are in a stable condition".
IEC figures suggest around half of the almost nine million people registered to vote actually cast a ballot.
In recent months, there have been dozens of attacks on people involved in the election process, including candidates and voters.
It is also considered an important milestone ahead of a United Nations meeting in Geneva next month where Afghanistan is under pressure to show progress on "democratic processes".More news: Trump Defends Immigration Policy
Kandahar residents will choose 11 candidates out of 111 parliamentary candidates Saturday, a week after the rest of the country voted.
Voters also complained about problems with the voter lists and said that there had been problems with the biometric system.
Any citizen suspecting or witnessing fraud or irregularities should channel complaints through the relevant Afghan authorities, especially the Electoral Complaints Commission.
Similar issues were evident in Kandahar, the birthplace of the Taliban and a province notorious for ballot stuffing, with many polling sites in the city opening more than an hour late - despite assurances from IEC deputy spokeswoman Kobra Rezaei on Friday that "we are absolutely ready".
The parliamentary elections in southern Kandahar province were due to be conducted last Saturday but the voting was postponed due to the deadly incident in governor's compound.
The vote in Kandahar had been delayed by a week after the murder, on October 18, the controversial but respected provincial chief of police, general Abdul Raziq, a man of a strong anti-taliban regarded him as a bulwark against the insurgency in the south.