Motorcycle taxis, a common form of transport in the city, are being used by criminals to carry out attacks, Bujumbura's mayor Freddy Mbonimpa said.
One person was killed on Monday when men on motorbikes threw three grenades.
Burundi plunged into crisis last April when President Pierre Nkurunziza announced his third-term bid.
His decision sparked street protests, a failed coup attempt and tit-for-tat killings have become part of daily lives in some parts of the capital.
Security has been boosted after Monday's attacks with soldiers and police searching vehicles and people, the AFP news agency reports.
"Police found that criminals often carry grenades in bags or baskets," Mr Mbonimpa said.
The BBC's Prime Ndikumagenge in the Bujumbura says the ban on motorcycles will make life more difficult for people travelling to different parts of the city.
One cannot get between southern and northern suburbs without passing through the city centre, he says.
Mr Nkurunziza, who has been in power since a 2005 peace deal that ended a brutal civil war, won disputed elections in July.
More than 400 people have been killed since April and at least 240,000 have fled to neighbouring countries.
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Burundi has banned the use of commercial motorbikes from the centre of the capital, Bujumbura, in a bid to end violence in the city.