“It is not possible for the Electoral Commission to reach embassies for elections,” it said in a letter to Burundi’s embassies.
Several Burundians in the diaspora have told the BBC this is a violation of their rights, and are determined to find a solution.
About 13,000 citizens living abroad had registered to vote in presidential and parliamentarians polls scheduled for 20 May.
Burundian officials recently told the BBC they hoped the COVID-19 outbreak would not affect the election calendar.
Five people are reported to have contracted the virus in the country, one of whom has died.
Manampa, a Burundian living in Kenya, told the BBC it would be sad if he was led by a president he had not voted for over the next seven years.
He suggested that the government use new technology to allow Burundians abroad to vote without queuing in embassies, or simply postpone the elections until after the pandemic.
Five male candidates are running to replace President Pierre Nkurunziza, who has been in power since 2005.