UN Secretary-General Ban Ki-moon condemned the killings on Saturday in a Bujumbura bar and called for a full investigation.
"Preliminary reports suggest that the attack was conducted by persons in police uniform," said UN spokesman Stephane Dujarric.
The UN staff member, who was a Burundian national, was working for the UN Development Program.
Ban also called on Burundi's security forces to exercise maximum restraint during a "forcible disarmament campaign" that left several dead including a police officer.
The United Nations has repeatedly called for dialogue between the government and the opposition to end the crisis.
