Clashes broke out in the capital Bujumbura's Cibitoke district, an opposition area that has been one of the heartlands of protests against President Pierre Nkurunziza's defiant bid for a third term.
While police said the deaths followed gunbattles with an "armed group", witnesses said the police staged summary executions after being attacked.
More than 70 people have been killed in two months of protests and a failed coup attempt sparked by the president's bid, with almost 144,000 refugees fleeing into neighbouring nations.
Cibitoke was sealed off today by security forces, an AFP photographer said, and it was not possible to independently confirm police reports.
The clashes took place after a grenade was thrown at a police patrol, injuring two officers, a police official said speaking on condition of anonymity.
An AFP reporter who later entered the area after the shooting had ended saw the bodies of six people killed, including a moneychanger in his sixties and his two sons, shot in the head. All the dead were civilians.
Those fleeing the district said police were carrying out house-to-house searches for guns.
On polling day yesterday, some voting stations were also attacked by grenades, according to the police.
The election commission claimed an "enormous" turnout in the local and general elections, despite many polling stations appearing quiet.
Vote counting has been completed at a local level, the election commission has said, but it remains unclear when final results would be announced. The ruling party is expected to win a sweeping victory.
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