Mr Kikwete has been credited with boosting the nation’s economy, but his opponents say he has failed to tackle widespread poverty.
His main rivals in the poll are Willibrod Slaa, a former priest, and university professor Ibrahim Lipumba.
On Sunday, voters were also electing 239 members of parliament.
The election results are expected on Wednesday.
Zanzibar deal
More than 19 million people in the East African country were eligible to cast their ballots.
A total of 18 political parties were competing, with seven candidates vying for the presidency.
President Kikwete, of the governing CCM party, was elected with more than 80% of the vote in 2005 and is now expecting to win again.
On Saturday, thousands of his supporters danced and cheered during a rally in Tanzania’s commercial capital Dar es Salaam.
Mr Kikwete promises to reduce poverty, improve health, education and transport, says the BBC’s Josphat Makori in Dar es Salaam.
But Mr Kikwete’s critics accuse his government of not living up to similar pledges during his first term, our correspondent says.
More than 50% of Tanzanians still live below the poverty line, according to the IMF.
On Sunday, voters in the Indian Ocean archipelago of Zanzibar – which enjoys a degree of autonomy from Tanzania – also went to the polls.
They were electing their leaders for the first time since a power-sharing deal was struck between Zanzibar’s two main political parties.
The agreement was aimed at bringing to an end the violence that erupted during Zanzibar’s polls in 2000 and 2005.
Source: BBC