The cat and its owners – who live in England but remain anonymous – have made a full recovery.
It is the first confirmed case of animal infection with the coronavirus strain in the UK, after a small number in Europe, North America and Asia.
The government said there was no evidence to suggest the animal passed the disease on to its owners.
Instead, a government spokesperson said, “All available evidence suggests the cat contracted the coronavirus from its owners who had previously tested positive for COVID-19.
“The cat and its owners have since made a full recovery and there has been no transmission to other animals or people in the house. ”
A private vet initially diagnosed the cat with the feline herpes virus after its owners noticed it was in pain.
However, the sample was then tested for SARS-CoV-2 – the virus that causes Covid-19 – as part of a research program.
Follow-up samples confirmed that the cat was also co-infected with SARS-CoV2.
Downing Street said the cat had “a runny nose and some shortness of breath” which prompted her owners to go to the vet.
The cat was in England but no details were revealed.
No10 said the case followed animal infections in countries including France, the Netherlands, Spain, Italy, Germany, Denmark, the United States, China and Hong Kong .
The Prime Minister’s official spokesperson said: “There is no evidence that pets or other domestic animals directly transmit the virus to humans.
“All of the available evidence in this case suggests that the cat contracted this from its owners, who themselves had previously tested positive for Covid-19.”
He added, “If your pet is sick, you should keep him indoors until he is healed. If you are worried enough, of course you can take your pet to the vet.
Chief Veterinarian Christine Middlemiss said: “This is a very rare event with infected animals detected to date showing only mild clinical signs and recovering within days.
“There is no evidence to suggest that pets directly transmit the virus to humans.
“We will continue to monitor this situation closely and update our advice to pet owners if the situation changes. ”
Yvonne Doyle, Medical Director of Public Health England, said: ‘This is the first case of a house cat testing positive for COVID-19 in the UK, but should not be a cause for alarm.
“Investigation of this case suggests that the infection spread from humans to animals, not the other way around.
“At this time, there is no evidence that pets can transmit the disease to humans.
“In line with general advice on combating the coronavirus, you should wash your hands regularly, including before and after contact with animals. “