The British Veterinary Association said animals "can act as fomites" (objects that can become contaminated with infectious organisms) and could hold the virus on their fur if they are petted by someone who has contracted it.
"For pet owners who have COVID-19 or who are self-isolating we are recommending that you keep your cat indoors if possible, during that time," the BVA said in a statement. "The virus could be on their fur in the same way it is on other surfaces, such as tables and doorknobs."
The American Veterinary Medical Association is not issuing the same advice.
The British group said, however, that its main advice to pet owners was to practice good hand hygiene.
The British veterinary association stressed that it is not suggesting all cats should be kept indoors and said owners should do so "only if the cat is happy to be kept indoors," acknowledging that "some cats cannot stay indoors due to stress-related medical reasons."
There has been a tiny handful of incidents in which animals have themselves tested positive for COVID-19, including a tiger in Bronx Zoo, but even in those cases there is no evidence that animals can pass the virus to humans.
"It is very important that people don't panic about their pets. There is no evidence that animals can pass the disease to humans," the BVA said. "From the small number of cases it appears that dogs do not show symptoms, but cats can show clinical signs of the disease."
The greater concern is that infected owners pet their cats, who then leave the house and are petted or stroked by strangers.
But opinion is divided on whether pets can indeed carry the virus in that way.
The leading veterinary authority in the United States, the American Veterinary Medical Association, is not issuing the same advice to pet owners as its UK counterpart.
"It is important to remember that there is currently no reason at this time to think that domestic animals, including pets, in the United States might be a source of infection with SARS-CoV-2," the AVMA says on its website.
"Accordingly, there is no reason to remove pets from homes where COVID-19 has been identified in members of the household, unless there is risk that the pet itself is not able to be cared for appropriately. In this emergency, pets and people each need the support of the other, and veterinarians are there to support the good health of both," it adds.
"In theory, if a patient with a virus in their nose rubbed their nose and got a bunch of virus on their hand and then petted their dog ... and then another family member petted that dog in the exact same place and then rubbed their nose, maybe they could transmit it," Dr. John Williams, chief of the division of pediatric infectious diseases at the University of Pittsburgh Medical Center Children's Hospital of Pittsburgh, told CNN last month.
"But if you're living in a home with a person who has the virus, the risk factor is that human, not the pets," he added.
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