Long queues of voters waited throughout the day outside many of the 6,400 polling centres before the prolonged process of counting began, with preliminary results not due until April 24.
Whoever emerges victorious must lead the fight against the Taliban without the help of US-led combat troops, and also strengthen an economy reliant on declining aid money.
The country faces a politically-testing few months as it undergoes its first democratic transfer of power, and many Afghans fear a repeat of the fraud scandals that marred the last presidential election in 2009.
There were no major terror attacks during polling, and organisers hailed the election a major success, despite complaints that a shortages of ballot papers had denied some citizens to right to vote.
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"Today, I can claim that the enemies of Afghanistan have failed in their plan to disrupt the election process," Interior Minister Omar Daudzai told reporters.
"People's participation in the election was unprecedented and it was a huge success."
The final turnout could exceed seven million, the head of the Independent Election Commission (IEC), Ahmad Yusuf Nuristani, said, though this was a preliminary estimate and may change. Initial predictions in 2009 proved inaccurate.
There was no clear favourite among the front-runners to succeed Karzai -- former foreign minister Zalmai Rassoul, Abdullah Abdullah, who was runner-up in the 2009 election, and former World Bank academic Ashraf Ghani.
The open nature of the race coupled with a massive security operation to thwart Taliban attacks may have contributed to the high turnout.
The Taliban had urged their fighters to target polling staff, voters and security forces, but there were no major attacks reported during the day.