Ms Banda had earlier said Tuesday's vote had been marred by rigging, multiple voting and computer-hacking.
She said a new vote should be held within 90 days but she would not stand again in any new poll.
However, correspondents say it is unclear whether the Malawian president has the power to order an election.
"I am nullifying the elections, using the powers invested in me by the Malawi constitution," Ms Banda told a news conference, according to Reuters.
"I want to give Malawians an opportunity to choose a candidate of their choice in a free and fair manner. When elections are to be held again, I will be stepping aside," she added.
Late on Friday, the Malawi Electoral Commission (MEC) said rival candidate Peter Mutharika had taken a lead of 42%, with 30% of votes counted. Joyce Banda was in second place with 23%, the commission said.
Mrs Banda had previously accused a party, which she did not name, of infiltrating and hacking the MEC's counting system.
The MEC's chairman denied that its system had been hacked.
Chaotic scenes
In a previous statement about the elections, Mrs Banda had said that irregularities included
The arrest of presiding officers who were "caught in the act of rigging"
Some people voting up to three times "Serious anomalies" where some candidates won more votes than the number of registered voters
Discarded and tampered ballots
Communication devices of some monitors being blocked
Voting had been chaotic, with one BBC correspondent reporting people voting two days on from election day because of delays in distributing election material.
Frustrated voters set one polling station alight and smashed election material at another.
In some places, voting boxes or lids did not arrive so officials used buckets and plastic wrap.
Around 7.5 million people were eligible to vote in the fifth elections since the end of one-party rule 20 years ago.
This was the first time that Malawi held presidential, parliamentary and local elections on the same day.
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