Burundi's government says BBC and VOA broadcasts will be banned for six months from 7 May for "falling short of laws governing the press" and "breaching professional ethics".
It accuses the BBC failed to challenge a Burundian activist interviewed on its French service.
The BBC broadcasts to Burundi on FM relay stations and on two local partner stations.
The country is gearing up for a referendum vote on 17 May, which could extend the rule of President Pierre Nkurunziza until 2034.
Human Rights Watch says Burundi government forces and members of the ruling party have killed, beaten and intimidated people they regard as opponents of the poll.
The US State Department recently said the vote could hurt Burundi's democratic institutions.
A number of private radio stations have been destroyed and shut down in Burundi during a political crisis which began in 2015, when President Nkurunziza won a controversial third term in office.
Since then, nearly 430,000 people, including opposition politicians, have fled Burundi.
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