There is one wild cat species in Japan – specifically on a Japanese island: Iriomote-jima. It is remarkably close to Taiwan and quite far from Japan as it happens. The cat is named after the island: Iriomote cat (scientific name: Prionailurus bengalensis ssp. iriomotensis). It is a subspecies of the Asian leopard cat (leopard cat), which is the wild cat ancestor of the famous, domestic Bengal cat. The Iriomote cat is Critically Endangered. There is habit loss on the island making things worse.
I have a nice page on this cat species so I want go over the detail here. Please click on this link if you are interested in reading and seeing more.
See also a world map showing the species per country.