Mrs Banda came to power two years ago after the sudden death of President Bingu wa Mutharika.
Her reputation has been dented by a corruption scandal, known as Cashgate, which has led donors to cut aid.
Her main challengers are Mr Mutharika's brother, Peter, Atupele Muluzi - the son of another former president - and a former preacher, Lazarus Chakwera.
By Chakuchanya  HarawaBBC Africa, Blantyre
Competitive election
Mr Chakwera is the candidate of the Malawi Congress Party, which governed from independence in 1964 until the first multi-party poll in 1994.
Voting was delayed in parts of the largest city, Blantyre, due to a shortage of election material.
"There's no ink. We're still waiting for the consignment," one of the officials told the crowd, reports the Reuters news agency.
There are reports of angry scenes at some polling stations.
But in the capital, Lilongwe, voting mostly started on time, Reuters reports.
Mrs Banda has denied any wrong-doing in relation to Cashgate and last week told the BBC that the fact the affair has gone to court was her "greatest achievement" because in the past, such scandals would have been covered up.
Scores of officials, including former ministers, have been arrested over the scandal, often with large amounts of cash. Up to $250m (Â£150m) may have been lost through allegedly fraudulent payments.
Analysts say that despite the close race, she is likely to win because of her popularity in rural areas.
The candidate with the most votes is declared the winner of the presidential race - there is no run-off.
There is a total of 12 presidential candidates.
Parliamentary and local elections are being held at the same time.
Malawi is one the poorest countries in the world and is heavily dependent on aid, with donors proving 40% of the budget.

In the 1960s and 70s, the spirits of scores of convicted Japanese war criminals were "enshrined" there.
The most controversial were the 14 "Class A" war criminals, including wartime leader Hideki Tojo, who were "enshrined" in the late 1970s.
These men were the ones who ordered and oversaw Japan's brutal war in China and South East Asia.
Yasukuni Shrine
It was a war in which millions died, in which there were widespread massacres of civilians, in which rape was routinely used as a weapon and where Japan used chemical and biological warfare against civilians.
So if the shrine is so offensive to China and South Korea why did Mr Abe go?
Firstly, because he wanted to.
Close observers of the Japanese prime minister say he is at heart a nationalist and a historical revisionist.
He believes the trials that convicted Japan's wartime leaders were "victors' justice".
His own grandfather Nobusuke Kishi served in the war cabinet and was arrested by the Americans on suspicion of being a Class A war criminal. He was later released without charge.
But the stain of association with Japan's war crimes in China never completely went away.
Secondly, Mr Abe's support base comes from the right wing of the Liberal Democratic Party.
According to Professor Jeff Kingston of Temple University in Tokyo, Mr Abe is "showing he is a tough guy", that he is not afraid of China. It is something that plays very well to his base.
But there is perhaps a bigger goal that Mr Abe has in mind.
He wants to radically revise Japan's post-war constitution.
This, too, is a long-held dream that started with his grandfather in the 1950s.
Mr Abe believes he is the man to complete the historic task of getting rid of the hated "peace constitution".
Like many on the right here, Mr Abe believes that constitution was forced on Japan by America and is a humiliation.
It imposes not only pacifism, but also Western notions of human rights and civil liberties. It rejects Japan's uniqueness in favour of "universal values".
Mr Abe would like to change a lot of this. But it will be very hard. And so he will need some help.
"Abe has provoked China, and China has reacted just as Abe wanted it to," says Prof Kingston. "There is a shrewd political calculus at work here."
What he means is that having an external threat in the shape of big and frightening China may be just what Mr Abe wants to help push through his controversial nationalist agenda at home.
Malawians have voted in a tight election, with President Joyce Banda facing three strong challengers.
[NEXT_CONCEPT]
Whatever Shinzo Abe says, any visit to the Yasakuni shrine by a Japanese prime minister is deeply political and sure to cause offence.