Explosions rang out in several neighbourhoods of Bujumbura. Locals told Reuters most of the dead were civilians and some had been found with their hands tied behind their backs.
Opposition groups have accused the government of launching a crackdown since crowds first took to the streets in May, saying President Pierre Nkurunziza's bid for a third term in office broke the central African state's constitution.
Nkurunziza, who went on to win a July 21 vote, last week acknowledged the judiciary had uncovered cases of security officers killing and torturing people. Days earlier the UN human rights chief said there had been an "alarming upsurge" in arrests and deaths.
Some of Nkurunziza's allies have also been killed in attacks. Officers who launched a failed coup in May, have said they will fight on to oust him.
Residents said the latest violence started late on Saturday afternoon and went into the night, with the worst of it in the Cibitoke and Mutakura neighbourhoods north of the capital, a focus for protests against the president.
"In total eight people have been killed; six in Cibitoke and two others in Mutakura neighbourhoods. Police officers were also wounded," Rémy Barampama, the head of Ntahangwa district in which Mutakura and Cibitoke fall, told Reuters.
Residents said more than eight people had died and most of them were unarmed civilians, including one disabled man who used a cane.
One Mutakura resident told Reuters locals had counted 10 dead, including one soldier, in their neighbourhood alone.
Burundi has been locked in its worst political crisis since its civil war ended a decade ago.
Under agreements that ended that conflict in 2005, presidents were limited to two terms in Burundi, a nation with a similar ethnic mix to neighbouring Rwanda, were 800,000 people died in a genocide in 1994.
Nkurunziza argues that a court ruling cleared the way for his election bid.