Mammalian predators introduced to oceanic islands pose a significant threat to biodiversity and have led to numerous extinctions. Free‐ranging cats are particularly problematic due to their predatory habits and negative impact on conservation. However, there is limited information on the ecology and population status of free‐ranging cats in insular ecosystems, where they often represent the apex terrestrial predator. Using a peri‐urban protected area in the subtropical island of Madeira as a case study, we employed camera traps to assess the density of free‐ranging cats and investigate the ecological drivers influencing their abundance and activity in nonurban insular habitats. Based on 582 trapping‐nights, we identified 25 individual cats from 156 cat detections. Spatially explicit capture–recapture models revealed a density of 1.4 cats per km2. Cat activity was positively affected by both the proportion of rocky areas in the landscape and the distance to human resource subsidies, whereas no significant driver was found for abundance. Our results indicate that cats are highly abundant throughout the protected area and suggest that their core home ranges are associated with rocky terrain, away from the most humanized sections of the park. Free‐ranging cats do not appear to heavily rely on anthropogenic food sources, signaling that they may rely mostly on wild prey to fulfill their dietary needs. Their preference for rocky areas could be explained by the increased availability of shelter and prey, such as the Madeira wall lizard (Teira dugesii). Notably, cat abundance and activity were particularly high in the vicinity of the only known breeding colony of the locally threatened Manx shearwater (Puffinus puffinus) on Madeira Island. Our findings suggest that cats pose a significant threat to the native vertebrate fauna of the protected area and thus their management, particularly during the breeding season of the Manx shearwater, should be considered.