Major roads throughout southern Kandahar were closed almost 24 hours before polls opened to stop vehicle-born explosive devices from entering the province, said provincial governor's spokesman Aziz Ahmed Azizi.
Voting started at 7.00 a.m. local time [0230 GMT] and is due to end at 4.00 p.m. local time [1230GMT], according to Nematullah Wardak, head of the country's Independent Election Commission (IEC).
No group has claimed responsibility for the blast, which took place as thousands of ballot boxes are being delivered to the IEC following the war-torn county's parliamentary elections.
Afghanistan's parliamentary elections were held against a backdrop of violence, with a multitude of attacks killing at least 36 people.
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Kandaharians will cast their votes in 173 polling stations across the province. Ibrahimi said 111 candidates were vying for 11 seats in Parliament from southern Kandahar in Afghanistan's 249-seat chamber. "They can not find people's names on the voters' list".
Unofficial election results of the parliamentary balloting are not expected before mid-November and official results sometime in December.
The suicide bomber was shot by the security forces but that could not prevent him from detonating, said Mujahid.
Voting in the province was delayed by one week after an attack that killed two senior Afghan officials. "Doubtless that a number of candidates wanted to use these people for their own benefit in the elections", said Danish.