It comes after the first case was confirmed last week on the island in north Wales.
The Welsh Government said a 3km protection zone and 10km surveillance zone have been declared around the infected premises, in order to limit the risk of the disease spreading.
It added that bird movements and gatherings are restricted to these zones and that all holdings must be declared.
Farmers are being urged to consult a vet if birds become unwell and if avian influenza is suspected, then it must legally be reported to the Animal and Plant Health Agency.
High levels of biosecurity are being encouraged for birdkeepers and they have been urged to remain vigilant.