Polling ended after a night of gunfire and explosions that claimed two lives in the capital Bujumbura.
The US State Department has joined critics saying the disputed presidential election lacks credibility and will discredit the government.
The government accuses the opposition of provoking violent protests.
President Nkurunziza is running for a third term despite a limit of two terms in the constitution.
The US said it would review all aspects of its partnership with the east African country including imposing visa restrictions on those it said were responsible for promoting instability.
The BBC’s Maud Julien in Bujumbura said gunfire could be heard in at least one district of the capital as polling stations opened on Tuesday morning.
Two policemen were shot dead in the capital on Monday night, said Willy Nyamitwe, the president’s chief communications adviser.
The body of an opposition official was found earlier on a road.
The president’s office described the latest protests as terrorist acts intended to disrupt the election.
In opposition areas of the capital, among the few who voted many tried to wipe off the indelible ink on their fingers fearing reprisals from opposition supporters.
Meanwhile, a high turn-out was reported in Mr Nkurunziza’s hometown of Ngozi in northern Burundi where he voted after riding to the polling station on a bicycle.
Three minor opposition leaders are running for the presidency. Mr Nkurunziza’s four main rivals, including Agathon Rwasa, are boycotting the poll, but the electoral commission has kept their names on the ballot paper.
The African Union (AU) did not send observers – the first time it has taken such a stance against a member state.
It said the security climate did not allow for free and fair elections.
The European Union has expressed a similar view, and has cut some aid to Burundi to show its anger with Mr Nkurunziza.
At least 70 people have been killed in protests since he announced in April that he was running for a third term.
About 1,000 people are fleeing into Tanzania each day to escape the violence, according to medical charity Medecins Sans Frontieres (MSF).
It said many families were crossing “on foot without any belongings”.
In May, army generals opposed to Mr Nkurunziza’s continuing rule failed to overthrow him in a coup.
Critics say that a win for President Nkurunziza would be a hollow triumph that will result in him governing a bitterly-divided nation.
Tensions between Burundi’s ethnic Hutu majority – comprising some 85% of the 10.5 million population – and the country’s Tutsi minority have flared up regularly since independence from Belgium in 1962.
Mr Nkurunziza led a Hutu rebel group fighting the Tutsi-dominated army until a peace deal led to him becoming president in 2005.
The Constitutional Court has backed his argument that his first term in office did not count towards the two-term limit, as he was elected by MPs.
Some 3.8 million Burundians were eligible to vote.