Local activists accused the police and soldiers of opening fire as the refugees protested over the plan in the town of Kamanyola in eastern Democratic Republic of Congo on Friday.
Six members of the Congolese security forces were killed in the clashes, Congolese army spokesman Dieudonne Kasereka said.
He said 34 people were killed, 15 of them women.
The coordinator of the U.N. Communications Group in Congo, Florence Marchal, confirmed a provisional death toll of 18, with 50 others wounded.
The Congolese government, the U.N refugee agency and the United Nations peacekeeping mission in Congo "have deployed teams on site to shed light on everything that happened", she said.
In the wake of the killings, Burundi's Foreign Minister Alain Aimé Nyamitwe took to Twitter demanding answers. The death of the Congolese army officer led to "the escalation of violence".
Out of 40,000 Burundian asylum-seekers, 28,000 who fled hostilities in their country were identified by the DRC's National Commission for Refugees in Kamanyola.
At least 124 refugees were also wounded.
More than 100 people were injured in the incident, according to Bertin Bisimwa, chief of Kamanyola. A total of 43,769 Burundian refugees live in DRC.
More than 400,000 refugees from Burundi have fled to neighboring Congo since 2015, to escape an outbreak of political violence that was sparked by President Pierre Nkurunziza's successful but disputed bid to win a third term in office.