Islands are biodiversity hotspots that host unique assemblages. However, a substantial proportion of island species are threatened and their long‐term survival is uncertain. Identifying and preserving vulnerable species has become a priority, but it is also essential to combine this information with other facets of biodiversity like functional diversity, to understand how future extinctions might affect ecosystem stability and functioning. Focusing on mammals, we (i) assessed how much functional space would be lost if threatened species go extinct, (ii) determined the minimum number of extinctions that would cause a significant functional loss, (iii) identified the characteristics (e.g., biotic, climatic, geographic, or orographic) of the islands most vulnerable to future changes in the functional space, and (iv) quantified how much of that potential functional loss would be offset by introduced species. Using trait information for 1474 mammal species occurring in 318 islands worldwide, we built trait probability density functions to quantify changes in functional richness and functional redundancy in each island if the mammals categorized by IUCN as threatened disappeared. We found that the extinction of threatened mammals would reduce the functional space in 63% of the assessed islands, although these extinctions in general would cause a reduction of less than 15% of their overall functional space. Also, on most islands, the extinction of just a few species would be sufficient to cause a significant loss of functional diversity. The potential functional loss would be higher on small, isolated, and/or species‐rich islands, and, in general, the functional space lost would not be offset by introduced species. Our results show that the preservation of native species and their ecological roles remains crucial for maintaining the current functioning of island ecosystems. Therefore, conservation measures considering functional diversity are imperative to safeguard the unique functional roles of threatened mammal species on islands.