It comes after a last-minute decision to declare Tuesday a holiday failed to persuade people to cast their ballots.
A low turnout threatens to undermine the legitimacy of former military chief Abdul Fattah al-Sisi, who is expected to easily beat leftist Hamdeen Sabahi.
The retired field marshal overthrew President Mohammed Morsi last July.
He has since been locked in a battle with Mr Morsi's Muslim Brotherhood, which has urged a boycott of what it calls "the election of blood".
Liberal and secular activists, including the 6 April youth movement which was prominent in the 2011 revolution that ousted Hosni Mubarak, have also shunned the poll in protest at the curtailing of civil rights.
Mr Sabahi said that his team had recorded "violations" in the voting process but rejected calls by his supporters for him to withdraw.
"We will not withdraw and, at the same time, we will not accept elections to be rigged," he said in a statement.
The election commission said voting had been extended to "allow citizens who could not cast their ballots because of residence restrictions" to participate, and reminded those who did not that they would be fined.
But reports from Cairo on Wednesday morning suggested the authorities would struggle to boost turnout significantly.
Analysis, by Kevin Connolly, BBC News, Cairo
Abdul Fattah al-Sisi, along with the interim government, the official media and Egypt's powerful army have been acting for months as though this election was a formality with victory for him inevitable.
They may have overdone it to an extent which has alienated some Egyptians - and left even those who like Mr Sisi not seeing much point in voting.
At many polling stations, soldiers on security duty have outnumbered voters and others have seen no voters at all for hours.
Extending voting into a third day might look a little desperate - but it's tantamount to an official admission that turnout has been worryingly low for the authorities.
A win for Mr Sisi on a very low turnout would damage his authority as he takes office. It would be particularly embarrassing for him to secure fewer than 13 million votes. That was the number recorded by Mohammed Morsi, the elected Islamist president whose removal from office was led by Mr Sisi last year when he was still serving in the army.
The head of the election commission told MBC-Misr TV that estimates from Monday and Tuesday suggested 35% of Egypt's 54 million registered voters had cast their ballots.
That would be a significant drop from the presidential election run-off in 2012 narrowly won by Mr Morsi, which had a turnout of just below 52%.
A low turnout would cast doubt on Mr Sisi's claim that he has the support of a majority of Egyptians. He has said he wants 40 million voters, or 74%, to cast their ballots to show that "there is consensus on a national level".
Mr Sabahi's campaign said the extension of voting was unjustified.
It denounced the move as an attempt to "prevent Egyptians from expressing their opinion through manipulating the turnout rates and the voting percentages".
The election is being held amid tight security, with more than 250,000 police and soldiers on duty at polling stations across the country, according to the interior ministry.
Militants have killed hundreds of security personnel since the army overthrew President Morsi following mass opposition protests.
The militants say they have stepped up attacks in response to the state's subsequent crackdown on the Muslim Brotherhood, in which more than 1,400 people have been killed and 16,000 detained.
Mr Morsi and other senior leaders of the Brotherhood, which has been designated a terrorist organisation, are currently standing trial on a raft of charges. They strongly deny any wrongdoing.
Egypt's presidential election has entered a third day after the military-backed interim authorities extended voting in an effort to boost turnout.