It is not unheard of for zoo animals to contract disease from humans (think elephants and tuberculosis), in fact, it is not even unheard of for big cats to contract diseases from their keepers. In 2009, a group of cheetah were confirmed to have developed H1N1 after a keeper that was infected prepared their diets. Since we already know that domestic cats have contracted the novel coronavirus from their infected owner, it stands to reason that a tiger being cared for by an infected human would be able to contract COVID-19 as well.
As the COVID-19 pandemic continues, more questions have come up about pets, owners and disease sharing. This weekend, a Malayan tiger was confirmed infected with SARS-CoV-2.