An investigation by Sweden's National Veterinary Institute (Statens veterinärmedicinska anstalt, SVA) showed that the swans likely died from other causes, but also carried the same strain of bird flu that has been circulating around Europe since autumn.
“The find in Stockholm will not lead to us taking any precautions other than those that already apply, but of course we pay close attention to any developments," Ingrid Eilertz of Sweden's Board of Agriculture said in a statement.
"It is, as always, important that those keeping poultry or other birds are mindful of hygiene and disease protection so that the infection does not spread to their pets," she added.
Countries such as Germany, Britain, Italy and the Netherlands have reported cases of the H5N8 bird flu strain. The virus has devastated flocks of poultry in Asia but has never been detected in humans.
In December, officials in Germany ordered a mass cull of thousands of turkeys after a bird flu was found at a poultry farm in Lower Saxony.
The outbreaks prompted Sweden's Board of Agriculture to issue new guidelines, telling farmers to put birds indoors or in covered fenced zones.
According to Sweden's Public Health Agency (Folkhälsomyndigheten) the bird flu found in Stockholm is the same H5N8 strain that hit its European neighbours, a type of virus that does not affect people but is very contagious among birds.
The H5N1 strain of bird flu has killed more than 400 people, mainly in southeast Asia, since first appearing in 2003.
Another strain of bird flu, H7N9, has claimed more than 170 lives since emerging in 2013.
The H7N7 strain of avian flu severely hit the Netherlands in 2003 with health authorities destroying some 30 million birds in an effort to quash an outbreak.