The Department of Agriculture is urging poultry owners to remain vigilant for any signs of bird flu in their flocks.
Farmers are asked to maintain strict bio-security measures and report any disease suspicion to their nearest Department of Agriculture Veterinary Office.
All of the more than 5,000 birds at the farm that have not died from the disease will be culled, UK authorities said.
The UK government also announced it was restricting the movement of animals and animal products around the affected site.
The H5N8 subtype of avian influenza has been responsible for a number of outbreaks of disease in both wild birds and poultry in several European countries since the end of October.
Cases of H5N8 have been reported in France, the Netherlands and Sweden in recent weeks, in both migratory birds and at farms.
While bird flu can cause serious disease in poultry and other birds, no human infections with this virus have ever been reported world-wide and therefore risk to humans is considered to be very low, according to a statement from the Department of Agriculture.
An early warning system is in place with Birdwatch Ireland, the National Parks and Wildlife Service and the National Association of Regional Game Councils with regard to surveillance for signs of disease in wild birds.
The Department of Agriculture is closely monitoring and assessing the disease situation and is in close contact with the Department for Environment, Food and Rural Affairs in the UK on the matter.