The samples, from near Bishop's Waltham, contained the highly contagious H5N1 virus, according to the Department for Environment, Food and Rural Affairs (DEFRA).
Defra stated that all birds at the affected premises would be humanely culled.
A 3km (1.86-mile) protection zone has been introduced which places restrictions on birds being moved, alongside a 10km (6.2-mile) surveillance zone.
The wider 10km zone covers Bishop’s Waltham, Hedge End, Twyford, Wickham, and a part of Eastleigh.
Both zones were put in place on February 4 and it has not yet been confirmed when they will be removed.
Avian flu, also known as bird flu, is a type of influenza that spreads among birds.
England has experienced its largest-ever outbreak of the H5N1 virus, with 75 cases confirmed since the start of November.
The risk to human health is considered to be low but the UK Health Security Agency (UKHSA) stated that one person in the south west had the virus in January.
The UKHSA has urged people to not touch sick or dead birds to keep themselves safe from the flu.
The UK's veterinary officer, Christine Middlemiss, previously issued a statement urging farmers to play their part.
She said: 'We are seeing a growing number of cases in birds on both commercial farms and in backyard flocks across the country. Implementing scrupulous biosecurity measures will help keep your birds safe.'
According to the NHS website, the symptoms of bird flu include a high temperature, aching muscles, headache, and a cough or shortness of breath.