Mr Museveni’s two main challengers are veteran opposition leader Kizza Besigye and former Prime Minister Amama Mbabazi.
Ugandans are also voting in parliamentary and local elections.
Uganda’s election explained
Polls opened at 04:00 GMT on Thursday. More than 15 million people are eligible to cast their ballots.
A candidate needs to secure more than 50% of the vote to win outright and avoid a run-off with the second-ranked contender.
Human rights groups have reported an intensifying government crackdown on opposition leaders, their supporters and the media during the election campaign.
Mr Museveni, 71, has been in office since winning a five-year guerrilla war in 1986, and he is one of Africa’s longest-serving leaders.
His final term was meant to end in 2006, but in 2005 he won a campaign to lift the constitutional term limits.
Mr Besigye has unsuccessfully challenged his former comrade-in-arms in the last three presidential elections
Mr Mbabazi is another former ally of President Museveni. He served as prime minister in 2011-2014, when he was dismissed after announcing he would launch a rival presidential bid.
During the election campaign the two opposition candidates accused the president of corruption and criticised his economic policies.
Mr Museveni dismissed the allegations as fiction.
Major issues for voters also include persistently high unemployment and poor quality of public services