They added that there was no evidence the virus could be transmitted to humans.
Four herons and a duck with the H5N8 subtype of the virus were found near Lake Constance in Vorarlberg, a health ministry spokesman said. Further measures would be decided once it was clear how pathogenic the cases were.
This week more than 100 dead waterfowl - especially herons - have been discovered around Lake Constance, also in Germany and Switzerland.
Wild migrating birds can transmit bird flu to farmed poultry. Containment measures are being coordinated with German and Swiss authorities and could include banning farmers from allowing poultry outdoors, the ministry said.
Hungary's food safety authority said last week it had found traces of bird flu at a poultry farm in eastern Hungary and would destroy 9,000 turkeys to protect people living nearby from a strain it said was harmless to humans.