Police said the suicide bomber was on foot and detonated the explosives near the gate of the offices.
The incident happened at about 8:15am local time in PD9 in Kabul city, a spokesman for Kabul police chief confirmed.
After waiting a week to cast their votes, Kandahar residents have finally been able to post their ballots in this parliamentary election.
It was not immediately clear how many people were at the site at the time of the attack.
There was no immediate claim of responsibility for the attack, which comes as thousands of ballot boxes from around the war-torn country are delivered to the IEC's heavily fortified compound in Kabul following chaotic and deadly legislative elections.
Problems with untested biometric verification devices, missing or incomplete voter rolls and absent election workers following Taliban threats to attack the ballot forced Afghans to wait hours outside polling stations, many of which opened late or not at all.
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In a WhatsApp message, Taliban spokesman Zabiullah Mujahid said "tens of Afghan police and soldiers were killed" in the attack.
Voting in Kandahar was pushed back a week after police chief Gen. Abdul Raziq Achakzai was killed in a Taliban-claimed attack October 18, two days before the election.
IEC officials said 4,500 observers will monitor the election process in Kandahar and 6,000 staff have been hired in Kandahar for the election process.
On Saturday voters in Kandahar - the southern birthplace of the Taliban and a province notorious for ballot stuffing - went to the polls.
On October 20, Afghanistan held its much-delayed parliamentary elections, the provisional results of which will be announced on November 10 and final ones on December 20.
The war toppled the militant group; however, some 17 years on, the Taliban are still active in two-thirds of the country and involved in widespread militancy, killing thousands of civilians as well as Afghan and United States forces despite the presence of US-led foreign troops.