An explosion occurred near a polling station in the Afghan city of Kandahar, just an hour after voters began lining up to vote for a new president.
A senior provincial government official said three people were injured by the blast.
No militant group has taken responsibility.
The Taliban, which controls the country more than at any time since its rule was overthrown in 2001, has threatened voters to stay away from elections or risk being injured.
There are 14 candidates registered in the election, but the main candidates are President Ashraf Ghani and his former Vice President Abdullah Abdullah.
The winner will play a pivotal role in the country's pursuit of an end to the Taliban war and the resumption of negotiations between hardline insurgents and the United States, which were canceled earlier this month.
Fear and frustration with the relentless corruption that characterized successive governments are among the concerns of Afghanistan's 9.6 million eligible voters.
Tens of thousands of Afghan National Army police, intelligence officers and personnel were deployed across the country to protect the 4,942 polling centers.
Authorities said 431 polling centers would remain closed because it was impossible to guarantee their security because they were in areas under Taliban control or where insurgents could threaten nearby villages.