Hybrid cats-created by crossing different species within the family Felidae-are popular pets, but they could potentially threaten native species if they escape and establish free-roaming populations. To forestall this possibility, the Australian government imposed a specific ban on importation of the savannah cat, a hybrid created by crossing the domestic cat Felis catus and serval Leptailurus serval, in 2008. We develop a decision-framework that identifies those species of non-volant native mammals in Australia that would likely have been susceptible to predation by savannah cats if importation and establishment had occurred. We assumed that savannah cats would hunt ecologically similar prey to those that are depredated by both the domestic cat and the serval, and categorised native mammals as having different levels of susceptibility to predation by savannah cats based on their size, habitat range, and behaviour. Using this framework, we assessed savannah cats as likely to add at least 28 extant native mammal species to the 168 that are known already to be susceptible to predation by the domestic cat, posing a risk to 91% of Australia’s extant non-volant terrestrial mammal species (n = 216) and to 93% of threatened mammal species. The framework could be generalised to assess risks from any other hybrid taxa.