Nandi-Ndaitwa’s main challenger is Panduleni Itula of the Independent Patriots for Change (IPC) party, along with 13 other candidates.
Local media reported that long queues had already formed at schools and other polling stations on Wednesday morning.
But there were also reports of a shortage of ballots in some polling stations.
Voting, which began at 07:00 local time (05:00 GMT), ends at 21:00.
Swapo has been in power since leading the country to independence in 1990.
A candidate needs more than 50% of the vote to win outright, otherwise there will be a runoff between the top two candidates.
The results are expected in the coming days.
Nandi-Ndaitwa cast her vote in the country’s capital, Windhoek, as polls opened, urging fellow Namibians to get out and cast their votes, saying it would “have an impact on the next five years of your life”.
She opposes the traditional political culture in a male-dominated country.
But she is a trusted leader, as she has served in high government positions for a quarter of a century.
Itula, a former dentist and lawyer, won 29% of the vote in the last election in 2019, trailing Swapo leader Geingob who got 56%.
He said it was an important day for Namibian democracy as he cast his vote in the capital.
Namibia is currently led by interim president Nangola Mbumba, who took office in February after Geingob’s death, but he is not running for office.
Analysts say the outcome may depend on youth, who make up more than half of the electorate.
Namibians are also electing new members of parliament.
Namibia is a vast and peaceful country with a small population of about three million, about half of whom have the right to vote.
