The National Liberation Forces (FNL), a former rebel group, was the ruling party's main competition until it pulled out of the election.
The voting was held against the backdrop of daily grenade blasts that threatened to push the country back into civil strife.
At least eight people have been killed and more than 60 wounded since opposition candidates pulled out of the race.
In the southern Bujumbura FNL bastion of Kanyosha, only a handful of voters had turned out to vote on Monday, compared to hundreds who voted in local council polls a month ago.
|Nkurunziza is the only candidate after six opposition candidates pulled out [Al Jazeera]
"At the moment, we can feel that the turnout is much lower than for the local council polls. There's a huge difference," Lydie Nzengou, chair of an international observation mission, said.
The East African Community (EAC) - of which Burundi is a member, together with Rwanda, Kenya, Uganda and Tanzania - urged all parties to ensure a smooth and democratic election.
The FNL has come under suspicion over the grenade attacks, with the police last week searching the home of the party's leader, Agathon Rwasa.
Speaking on condition of anonymity, a police official confirmed the search was linked to the violence.
"We have just carried out a search at Agathon Rwasa's home as part of our investigation into the spate of grenade attacks rocking the country," the official said.
The FNL has denied involvement in the attacks and has said that their leader is being targeted for political reasons.
Over the weekend, police also arrested six members of the opposition group the Movement for Solidarity and Development (MSD) in the capital, Alexis Sinduhije, chairman of the MSD, said.
A police spokesman said the suspects were named by an informant, who said they intended to disrupt the presidential poll.