The "Imbonerakure" -- whose name means "The Watchmen" -- has long been accused of using barbaric methods to achieve political ends on behalf of President Pierre Nkurunziza and his ruling CNDD-FDD party.
The explosion happened last evening in a house in the Musaga district of Bujumbura which residents said serves as a neighbourhood headquarters for the youth wing.
Municipal police commissioner, Bonfort Ndoreraho, confirmed that the victims were members of the Imbonerakure and said the perpetrator was "not yet known".
Rights groups have detailed abuses by Imbonerakure members accusing them of intimidation, torture, rape and murder of government opponents.
Burundi's sometimes violent political crisis has caused 400,000 to leave the country and left hundreds dead since 2015.