Museveni, 81, is widely expected to win a seventh term in office thanks to his total control of the state and security apparatus.
The election is being closely monitored both locally and internationally amid intense political competition and renewed calls for transparency.
Polling stations in several parts of Uganda were still not open in many areas almost two hours after voting was due to start, AFP journalists and local sources said Thursday.
Still haunted by the tyrannical reign of Idi Amin, Uganda has been involved in several civil wars and regional conflicts since achieving independence from Britain in 1962.
Uganda is on edge as polls opened on Thursday, with President Yoweri Museveni expected to extend his 40-year rule amid an internet shutdown and a police crackdown on the opposition.
During his bush war era, Museveni was insistent that Uganda needed a clean break from leaders who mistook the state for themselves and that power belonged to the people.