All birds at the site, which is centred on Highleadon near Hartpury College, are to be humanely killed, said the Department for Environment, Food and Rural Affairs (DEFRA).
Under new restrictions, the 3km protection zone was set up from Sunday night, preventing the movement of any birds or eggs within or out of the zone to prevent the spread of the H5N1 strain of bird flu, which has been found at 29 sites in England up to yesterday (Tuesday, December 7).
A wider 10km surveillance zone has also been put in place around the premises, tightening restrictions on bird movements.
Letters will be sent to houses and commercial properties within the 3km zone, which includes Rudford, Tibberton, Kent’s Green and Hartpury, detailing what action needs to be undertaken.
Residents and businesses will need to notify any poultry on their premises and to avoid moving poultry in and out of the zone.
Since November 29 it has been a legal requirement for all bird keepers to keep their birds indoors and to follow strict biosecurity measures in order to limit the spread of the disease.
DEFRA said that wild birds migrating to the UK from mainland Europe during the winter can carry the disease which can lead to cases in poultry and other captive birds.
"There is no impact on the consumption of properly cooked poultry products including eggs," DEFRA added.
National Farmers Union South West spokesman David George said: "Free range poultry across the country has been subject to a housing order since the end of November to help protect flocks against avian influenza (AI), which is generally spread by migrating birds and has become common at this time of year.
"So, whilst this outbreak is unfortunate, it is not entirely unexpected."
The NHS said the strain does not infect people easily and is not usually spread from human to human, although there have been isolated cases of people being infected around the world, leading to some deaths.
People should not touch or pick up any dead or sick birds they find and should report them by calling 03000 200 301.
The rules in the zones also cover the removal of litter, manure and slurry, and other biosecurity measures.
For full guidance, go to assets.publishing.service.gov.uk