Aim To investigate whether feral cats influence the distribution of Australia's largest remnant population of the threatened brush‐tailed rabbit‐rat Conilurus penicillatus and examine whether they influenced the extinction probability of C. penicillatus over a 15‐year period (2000–2015). Location Melville Island, northern Australia. Methods In 2015, small mammal surveys were conducted at 88 sites across Melville Island, 86 of which had previously been surveyed in 2000–2002. We used single‐season occupancy models to investigate correlates of the current distribution of C. penicillatus and dynamic occupancy models to investigate correlates of C. penicillatus local extinction. Results Our results show that C. penicillatus, which once occurred more widely across the island, is now restricted to parts of the island where feral cats are rarely detected and shrub density is high. Our results suggest that feral cats are driving C. penicillatus towards extinction on Melville Island, and hence have likely been a significant driver in the decline of this species in northern Australia more broadly. The impact of feral cats appears to be mitigated by vegetation structure. Main conclusions The ongoing development and implementation of methods to effectively reduce feral cat densities, coupled with the management of landscape processes to maintain shrub density, through fire management and the removal of large exotic herbivores, will contribute substantially to conserving this threatened species. This study demonstrates that the distribution of species can be strongly influenced by top‐down factors such as predation, thereby highlighting the importance of including biotic interactions when investigating the distribution of predation‐susceptible species.