Further tests are being carried out at a Suffolk farm to determine whether any more animals have been affected by the UK's first case of bluetongue disease.
The insect-borne virus, which has killed livestock across Europe, was in a Highland cow at the Baylham House Rare Breeds Farm, near Ipswich.
Sheep, cattle, goats and deer can be infected, but humans are not at risk.
In a statement, the family which runs the farm said they were "hopeful" about the future.
The bluetongue disease is not contagious but often leads to death in sheep.
Animals with it experience discomfort, with flu-like symptoms, and swelling and haemorrhaging in and around the mouth and nose.
They can also go lame and have difficulty eating properly.
Farmers say the arrival of the disease is devastating for an industry already struggling with foot-and-mouth.
There have been nearly 3,000 cases of bluetongue in Northern Europe - including the Netherlands, Belgium, France and Germany - since July, which had fuelled fears of its arrival in the UK.
Tests have shown the UK case is serotype eight - the same strain of the disease which has affected animals recently in Northern Europe.
BLUETONGUE IN CATTLE
Swelling of the head and neck
Swelling of the mouth
Debby Reynolds, chief veterinary officer, said: "It remains vitally important that farmers maintain vigilance for this disease and report any suspect cases, particularly as clinical signs may be similar to foot-and-mouth disease."
The government's deputy chief veterinary officer, Fred Landeg, confirmed the infected cow was on a small cattle and sheep farm outside Ipswich.
The infected cow's carcass has been removed from the farm. Tests on other livestock are being conducted.
It would not be classed as an outbreak unless other cases were confirmed, Mr Landeg said.
The farm is run by Richard, Ann and Neil Storer and as well as cattle, they have a collection of rare sheep, pygmy goats, chickens and pigs.
The Storer family statement said the cow which had contracted bluetongue was called Debbie.
It said: "We have lost Debbie, a Highland cow who was a great favourite with our regular visitors.
"However the future is hopeful and we are so grateful that we have not had to endure the terrible trauma that farmers in Surrey must be going through."
The family also described the veterinary teams from the Department for Environment, Food and Rural Affairs (Defra) as "wonderful".
Robin Richards, who owns the farm next to Baylham House, said he was braced for news his animals were infected.
"If he's got it I consider I must almost certainly have it because the midges must have come over our farm and that's how it spreads," he said.
He added his main concern was that the government would decide to cull livestock in the area.
If the virus has spread, Defra said it would impose a 20km (12.4m) control zone around the infected farm.
There would also be a 150km (93.2m) surveillance zone.
Defra said it was not imposing any additional movement restrictions above those currently in force due to the foot-and-mouth outbreak.
The discovery of bluetongue disease came after another case of foot-and-mouth disease was confirmed in Surrey.
On Saturday cattle on the sixth premises to test positive since the disease was first discovered in August - and the fourth in the past 11 days - were slaughtered and the protection zone extended.
Farming leaders said the discovery of bluetongue had come at a bad time for an industry already struggling with movement and export restrictions imposed because of foot-and-mouth.
National Farmers' Union president Peter Kendall said he was hopeful there would be no major outbreak.
"I'm optimistic this can be quite an isolated localised case and going into winter these midges aren't as active as they would have been if this had happened two or three months ago."
The effects of bluetongue can be severe, but animals can recover
The president of the British Veterinary Association, David Catlow, said he feared the disease may become prevalent in the UK.
"At the moment if this becomes established in the UK, as it seems to have become established in northern Europe, the only way we will really control it is when we have a vaccination, and that isn't yet available.
"We're possibly a year away before the development of some new, inactivated vaccines that will be the way ultimately to control it."
Bluetongue disease is transmitted by midges, traditionally the Culicoides imicola midge. It is passed from animal to midge, and from midge to animal, but is not transmitted from animal to animal.
The virus has long blighted Africa, but in recent years has begun to spread northwards into Europe.
Some scientists believe that climate change could be behind its spread, as warmer temperatures have seen the biting insects gradually move north.
Once infected, up to 70% of a flock of sheep can die from the virus. While infected animals can recover - and become immune - productivity is reduced with milk yields in dairy herds dropping by about 40%.
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