It was not immediately clear how many people were at the site at the time of the attack.
The province's powerful provincial police chief, Gen. Abdul Raziq, was killed, as well as at least another provincial official and several policemen.
In a WhatsApp message, Taliban spokesman Zabiullah Mujahid said "tens of Afghan police and soldiers were killed" in the attack.
Kandahar Governor Zalmay Wesa was seriously hurt in the October 18 attack that killed provincial police chief Gen. Abdul Raziq and also targeted the commander of U.S. and North Atlantic Treaty Organisation troops in Afghanistan, Gen. Scott Miller, who escaped unhurt.
Bashir Ahmad, another resident of Kandahar, who is disabled and came to cast his vote, called voting vital for the future of Afghanistan and criticized the IEC for not starting the process on time.
The election commission has also said that 567,000 people have registered to vote in Kandahar.
The UN-backed government is rife with corruption and many Afghans have said they do not expect the elections to be fair.
Dodgers win longest World Series game ever 3-2
Innings: The game went 18 innings , four more than the previous record of 14 that occurred three times - 1916, 2005 and 2015. Moreland's blast traveled 437 feet, only two shy of Puig's big blow, and pulled the Red Sox within one.
Unofficial election results of the parliamentary balloting are not expected before mid-November and official results sometime in December. They are also high for the US, which is still seeking an exit strategy after 17 years of war that has cost more than $900 billion and claimed the lives of more than 2,400 USA service personnel.
A suicide bomber targeting the headquarters of Afghanistan's Independent Election Commission (IEC) on Monday killed at least one person and wounded six, officials said, in the latest violence to strike the controversial poll.
No individual or group has so far claimed responsibility behind the incident.
IEC figures show around four million people voted in last weekend's parliamentary election that was held in 32 out of 34 provinces after months of chaotic preparations.
But some polling centers had still not opened by 8am, while dozens of people lined up outside.
Ghazni elections were delayed for an as yet indefinite period due to disagreements over constituencies and security issues.