Organisers appeared unprepared for such a high turnout in a country where many people defied intimidation from the Taliban to exercise their rights.
The Independent Election Commission ordered voting to be extended by at least an hour, with ballot papers being dispatched where they were needed for people to vote for a successor to President Hamid Karzai.
Organisers of the vote - the first democratic handover of power in Afghan history - had feared that a low turnout and Taliban violence would derail the election but as polling stations began to close, those fears had not materialised.
"People did not expect this number of people to come out to vote," said Toryalai Wesa, governor of the southern city of Kandahar. "They though the turnout would be similar to the past and that's why they sent fewer voting materials this time."
In the capital, Kabul, many polling stations decided to extend voting hours way beyond the official closing time of 4pm to allow voters to cast their ballots.
In the western Dasht-e-Barchi neighbourhood of Kabul a line of hundreds of men and women snaked outside one polling station, with many impatient voters saying they had been waiting in the rain for most of the day.
"I have waited here for hours, but was not allowed inside to vote because there is no ballot paper," said Hassan, who only gave his first name, as others nodded in agreement. "This is a deprivation of my right and I am unhappy at not being able to take part in this historic process."
Mohammad Hashimi, an election observer, added: "Many people stood in the rain for hours but couldn't vote because of the [lack of] ballot papers."
Ahmad Yusuf Nuristani, chairman of the Independent Election Commission, told reporters that signs were that the turnout was good, while acknowledging the foulup over ballot papers.
"The report we have so far indicates that many people participated in these elections and even in some stations we ran out of ballot papers," he said. "We have already sent some ballots to those stations which we had reserved in provinces."
Of the eight candidates contesting the presidency, the three frontrunners to succeed Karzai - who is barred by the constitution from running again - are former foreign ministers Abdullah Abdullah and Zalmay Rassoul and former finance minister Ashraf Ghani.
Most obesrvers believe no candidate will win at least 50% of the votes, meaning that a runoff election will need to be held on May 28.
A smooth election with a high turnout is good news for Afghanistan's Western backers who are watching the vote closely in order to decide whether to continue to extend billions of aid desperately needed to support Afghanistan's ailing economy.
It was not immediately clear how widespread the shortage of ballot papers was around the country. Afghanistan has 12 million eligible voters, and officials say there were 15 million ballot papers printed.
There was no official estimate of the turnout, but at the last election in 2009, the turnout of 4.6 million was regarded as low.
Because of Afghanistan's difficult terrain, it will take weeks for officials to gather ballot boxes from around the country and count the votes. Official preliminary results are not expected until late April.