The latest cases come a day after a dead wild duck in Wales was found to have the same dangerous strain of the disease.
A highly-pathogenic H5N8 strain of avian flu that was found in a turkey farm in Lincolnshire last week and has been circulating in Europe.
Following the latest discovery, Public Health England insisted the risk to the public was very low. Poultry and poultry products such as eggs are safe to eat as long as they are properly cooked.
A temporary ban on events involving gatherings of poultry including chickens, turkeys, ducks and geese such as auctions and livestock fairs has been imposed across England, Scotland and Wales to prevent spread of the disease.
A prevention zone is also in place, which requires keepers of poultry and other captive birds to keep them inside or take appropriate steps to keep them separate, and protect them, from wild birds.
Experts have said the threat to public health from the virus is very low.
Scottish Rural Economy Secretary Fergus Ewing said: “With the recent disease confirmations in both England and Wales, it is not unexpected for avian influenza to be found in a wild bird here in Scotland.
“We have already made clear that all bird keepers - whether major businesses or small keepers with just a few birds - must ensure that their biosecurity is up to scratch and prevent any contact between their birds and wild birds.”
There is said to be strong evidence from Europe that the disease is getting into housed poultry, the Press Association reported.
The Scottish Government said that experience with previous outbreaks has also shown that during periods of excessive rainfall, such as expected with Storm Barbara, there is an additional risk of run-off water carrying contaminants into poultry houses, bringing contaminated material into closer contact with poultry.
Scotland’s Chief Veterinary Officer Sheila Voas said: “This case of H5N8 in a falcon in Dumfries and Galloway confirms that avian influenza is present in wild birds in Scotland.
“This underlines the crucial importance of bird keepers and members of the public remaining vigilant for signs of disease in domestic or wild birds.
“Expert advice remains that consumers should not be concerned about eating eggs or poultry and the threat to public health from the virus is very low.”
Further updates on wild bird testing will be provided by the Animal and Plant Health Agency on their website.
UK Chief Veterinary Officer Nigel Gibbens said: “Today’s confirmed findings mean that avian flu has now been found in wild birds in widely-separated parts of England, Wales and Scotland.
“This is far from unexpected and reflects our risk assessments and the measures we have taken including introducing a housing order for poultry and a ban on gatherings.
“We’ll continue to work with ornithological groups to further strengthen surveillance and our understanding of the extent of infection in wild birds.