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.
Malawians have voted in a tight election, with President Joyce Banda facing three strong challengers.