Burundi has banned motorbikes from the centre of the capital on Tuesday after a string of grenade attacks by insurgents on motorcycles, the mayor said.

On Monday, men on bikes threw three grenades in the heart of the city, while two other blasts were reported in a northern suburb, killing a child and wounding some 30 people.

"Having seen that it is these motorcycle taxis that often carry the criminals who explode grenades in the city, we decided to ban them from the centre of Bujumbura," city mayor Freddy Mbonimpa said.

Motorbike taxis are a common form of transport in the city.

Medics from Doctors without Borders (MSF) on Tuesday said they had treated over 60 people wounded in the latest blasts, days after treating another 55 wounded on February 11.

Burundi plunged into crisis in April when President Pierre Nkurunziza ran for and won a controversial third term, sparking street protests, a failed coup, regular killings and a nascent rebellion.

Hundreds have been killed in the violence and at least 230,000 have fled the country.

Grenade blasts have become commonplace in the city, but it remains unclear who carries out the attacks, which have increased in the past two weeks. Security forces, rebels and opposition all blame each other for the killings.

Security was boosted Tuesday after the attacks — the latest in months of violence — with soldiers and police searching vehicles and people.

"Police found that criminals often carry grenades in bags or baskets," added Mbonimpa.

The leader of the failed May 2015 coup, ex-general Godefroid Nyombare, now leads a rebel group, Forebu.

The rebels formed the force "to protect the population" and uphold the Arusha Agreement that paved the way to the end of the country's 1993-2006 civil war — an accord they say Nkurunziza violated by his third term in power.