Voting was due to begin at 07am (0400 GMT) but the process was stalled for up to four hours in numerous polling stations where ballot boxes and papers did not arrive on time.
The long delays occurred especially in the capital Kampala, where the opposition usually gains many votes.
Election commission spokesman Jotham Taremwa said, “there was a bit of a delay at some polling stations because of logistical problems.”
At one Kampala polling centre, hundreds of frustrated voters shouted and gesticulated at election officials. “They are denying us our constitutional right,” said Elias Bukenya, a 27-year old teacher who suspected foul play.
Social media, including Facebook and Twitter, were largely inaccessible on voting day although Internet-savvy Ugandans dodged the apparent shutdown using virtual private networks.
Government regulator, the Uganda Communications Commission, said the attempted shutdown was for “security reasons” without giving details.
READ: Ugandan presidential polls open with delays
Museveni is widely predicted to win a fifth term, with the 71-year-old former rebel fighter who seized power in 1986 entering his fourth decade in power.
The strongest among seven challengers is Kizza Besigye, 59, who is making his fourth run at the presidency and ended his campaign claiming the election would be neither free nor fair.
At polling stations where voting got underway more or less on time, experienced voters turned up anticipating a long wait in the hot sun.
At Nakulabye in the capital Fred Musoke, 34, said, “I came ready – I packed tea and pancakes to wait until I vote.”