Opposition and civil society groups have denounced his candidacy as unconstitutional and a violation of the 2006 peace deal that ended a dozen years of civil war and ethnic massacres in 2006.
Hours before the polls were due to open, explosions and gunfire rang out late Monday in the capital Bujumbura, the epicentre of three months of anti-government protests.
AFP journalists heard at least three explosions and sustained bursts of gunfire shortly before 11:00 pm (2000 GMT).
Earlier Monday, a grenade was lobbed from a passing car into a street close to the symbolic Independence Square in central Bujumbura. There were no reports of injuries.
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Willy Nyamitwe, Nkurunziza's chief communications advisor, condemned the attacks as "terrorist acts" aimed at "intimidating voters".
Critics fear a win by the incumbent will be a hollow victory, leaving him ruling over a deeply divided nation.
With the elections denounced by the opposition as a sham, the 51-year-old president -- a former rebel, born-again Christian and football fanatic -- is facing no serious competition.
Around 3.8 million Burundians are eligible to vote between 06:00 (0400 GMT) and 16:00 (1300 GMT).