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The tiger, named Nadia, is believed to have caught the virus from an asymptomatic (someone who is not exhibiting symptoms) zoo keeper.
Bronx Zoo, based in New York, had the results confirmed by National Veterinary Services Laboratory in Iowa, US.
Nadia, along with her sister Azul, two Amur tigers and three African lions, began exhibiting symptoms late last month including a dry cough.
While the 260-acre zoo - which has over 600 species of animal - is currently closed in light of the virus outbreak, zoo keepers are still in contact with the animals for feeding and other forms of care.
"We tested the cat [Nadia] out of an abundance of caution and will ensure any knowledge we gain about Covid-19 will contribute to the world's continuing understanding of this novel coronavirus," the zoo confirmed in a statement.
"Our cats were infected by a person caring for them who was asymptomatically infected with the virus or before that person developed symptoms."
All the big cats showing symptoms were being kept in the zoo's Tiger Mountain area.
Despite some losses in appetite, the animals "are otherwise doing well under veterinary care and are bright, alert, and interactive with their keepers". All big cats are expected to make a full recovery.
As the number of global cases of COVID-19 stands at 1,287,168 as of 6th April, there have been few animal cases.
In late February, a Pomeranian dog became the first-known case of human-to-animal transmission of the virus.
The 17-year-old pooch, who has now sadly died, was reported to have a 'weak level' of the virus and was put in quarantine for 14 days.
The dog's owner, a 60-year-old woman, tested positive for coronavirus at the same time but has now recovered.
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