The birds account for nearly 10 per cent of the stock at the Thanh Binh facility in Phan Rang city of Ninh Thuan province, Dan Tri newspaper reported, quoting the Local Animal Health Agency.
Authorities were planning to cull all remaining birds at Thanh Binh and two other nest farms were H5N1 had been found, VietNamNet reported.
Experts and farmers have criticised the plan, calling for more time to examine the virus transmission mechanism, and pointing to the potential cost to the farmers.
Ninh Thuan province has many so-called bird houses, where the swifts are encouraged to build their nests, which are then collected for sale. The nests, made largely of the birds' saliva, are a sought-after ingredient for soup and other delicacies.
Vietnam on Tuesday confirmed a 12-year-old girl died after contracting the H5N1 virus, bringing the country’s fatalities from the virus this month to three.
In China, 20 people have died from a new strain, H7N9, which has not been recorded in Vietnam.