The domestic cat, Felis catus, is often cross-bred with other species in the cat family to produce hybrid or ‘designer’ cats that are sought by people as pets. However, hybrid cats are often surrendered to wildlife shelters, or released, which leads to concern that they may establish free-roaming populations and damage native wildlife. In 2008, the Australian government rejected an application, on precautionary grounds, to import savannah cats (hybrids of the domestic cat and serval Leptailurus serval) into the country. We review the limited information informing this decision and then present a framework that identifies the native mammal species likely to have been most at risk of predation from savannah cats if importation and establishment had occurred. Assuming that savannah cats hunt similar prey to those that are hunted by both parent species, we estimate that 91% of Australia’s extant terrestrial mammal fauna would likely face some risk of predation from savannah cats, including 93% of non-volant mammal species that have threatened conservation status. The framework results strongly validate the decision to ban savannah cats from Australia. We suggest that our framework approach could be adapted to assess the likely risks that are posed by the arrival of other hybrid cats or hybrids of other animals.