The tiger, named Nadia, is believed to be the first known case of an animal infected by a human with Covid-19.
The Bronx Zoo, in New York City, says the test result was confirmed by the National Veterinary Services Laboratory in Iowa.
Nadia, along with six other big cats, is thought to have been infected by an asymptomatic zoo keeper.
The cats started showing symptoms, including a dry cough, late last month after exposure to the employee, who has not been identified.
"This is the first time that any of us know of anywhere in the world that a person infected the animal and the animal got sick," Paul Calle, the chief veterinarian at the zoo, told Reuters news agency on Sunday.
He said he intends to share the findings with other zoos and institutions researching the transmission of Covid-19.
"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 said in a statement.
Nadia, her sister Azul, as well as two Amur tigers and three African lions who showed symptoms, are all expected to make a full recovery, the zoo said.
This case is being described as unusual because coronavirus transmissions from humans to animals have been rare and not well understood so far.
There is "no evidence that any person has been infected with Covid-19 in the US by animals, including by pet dogs or cats," the zoo statement noted.
That is also the view of the World Health Organization (WHO), which says there is no evidence that pet dogs or cats can pass on the coronavirus.
However, conservation experts have warned that the virus could pose a threat to some wildlife like the great apes - and have said measures are needed to reduce the risk of wild gorillas, chimps and orangutans.