So far, 31 people have died of the water-born disease in the area around the western Tanzanian border town Kaguna, which has been flooded with refugees, the UN refugee agency said.
All but two of those who have died were Burundian refugees, and most were children, it said.
"The situation is serious," Paul Spiegler, chief medical expert at the UN refugee agency, told reporters.
In Kaguna, the western Tanzanian border town with Burundi, on the shores of Lake Tanganyika, over 50,000 refugees are struggling in dire conditions.
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"At this rate, further cases can be expected over the next days and until the situation can be brought under control," he said, adding that the agency was working with the Tanzanian health ministry and other aid organisations to halt the outbreak.
Cholera is transmitted through contaminated drinking water, and UNHCR said overcrowding and unsanitary conditions in Kaguna, as well as the consumption of water directly from the lake, were believe to have sparked the outbreak.
The agency and its partners are struggling to move refugees from overcrowded Kaguna, situated on a narrow peninsula surrounded by a steep mountain range, to the western province of Kigoma, where the Nyanrugusu refugee camp is located.
While it is risky moving people with cholera, Spiegler said that due to the "horrible overcrowding" in Kaguna, aid organisations had determined more people would die if they were left there.
"We are expecting things to unfortunately get worse," he said, adding though that UNHCR hoped for a turn-around within a week.
UNHCR and its partners also launched an appeal to donors today for USD 207 million to respond to the crisis inside Burundi that has sparked the outflow of refugees.
Since early April, around 100,000 people have fled to neighbouring countries -- mainly to Tanzania -- and Edwards said estimates now show that number could double within the next six months.