Gunfire and explosions have been heard in the Burundi capital, Bujumbura, as voters take part in the first national polls since civil war began in 1993.
The polls are seen as a key test of Burundi's stability
One person was killed and another injured in a grenade attack on a polling station, the army said.
The local polls mark a key stage in power-sharing arrangements to end the war which pitted rebels from the Hutu majority against a Tutsi-led army.
A new parliament and president are due to be elected over the next two months.
Correspondents say the poll is a key test of Burundi's stability.
A South African peacekeeper was shot and wounded when the polling station he was guarding came under attack, says the UN mission in Burundi.
There is no confirmation yet of who is responsible for the violence.
It occurred in areas which have been the stronghold of Burundi's last active rebel group, the Hutu Forces for National Liberation.
The group agreed to end hostilities last month, but have since clashed with the army.
The violence has kept some voters away from the polls in the provinces of Bubanza and Bujumbura Rural. But in the rest of the country, voting was reported to be proceeding calmly.
Laid down arms
More than 3,000 councillors will be elected, who will in turn choose members of the senate.
The voting process guarantees all ethnic communities a share in power
Those elected to the national assembly next month will choose the president in August.
The last elections in Burundi in 1993 ended in disaster when Melchior Ndadaye, a Hutu, was elected president.
Shortly afterwards he was assassinated by Tutsi soldiers and the country was plunged into a civil war that killed some 300,000 people.
But now all but one of the Hutu rebel groups have laid down their arms and taken up politics.
Under pressure from African leaders, Hutu and Tutsi politicians have hammered out a unique deal which guarantees both communities a share in power.
These local elections, the first step in implementing that deal, are a test of strength between the two main Hutu parties, Front for Democracy in Burundi (Frodebu) and the former rebel Forces for the Defence of Democracy (FDD).
Both these parties have their sights firmly fixed on the greater prize - winning power at national level.
On Thursday, one of Burundi's main Tutsi parties - the Party for National Recovery - said it would not recognise the election results after it accused a rival Tutsi party - the Union for National Progress - of preparing to steal votes on a huge scale.
Correspondents say if these polls - and the parliamentary and presidential elections due to be held over the next two months - do pass off peacefully, Burundi will be seen to have turned the corner away from violence.
But the country still faces huge challenges: Bitter ethnic divisions remain and some from the Tutsi minority fear that Hutu parties will dominate the new Burundi.