Unidentified gunmen attacked the bar in Saga village, Rumonge province, at around 8:30 p.m. on Monday evening, regional official Joachim Manirakiza told Reuters.
Manirakiza said a school principal was among the victims.
The African country has been gripped by political strife and conflict since President Pierre Nkurunzizas sought and won a third term in 2015, which opponents said violated the constitution and terms of a peace deal that ended civil war in 2005.
At least three rebel groups have taken up arms against Nkurunziza and hundreds have been killed, including opposition figures and government officials, in tit-for-tat violence.
The UN Human Rights Council agreed last week to set up a commission of inquiry to identify perpetrators of killings and torture in Burundi and to ensure they are brought to justice.
At least 564 killings have been documented by the United Nations in Burundi since the unrest broke out.