Island mammals have influenced ecological and evolutionary theory since Darwin, and many of them provide textbook examples of the dramatic morphological evolution that often occurs in island communities. However, patterns of evolution in the climatic niches of island mammals have yet to be fully explored. Several hypotheses explaining niche divergence in island species have been introduced, linking niche evolution to increased competition among closely related or sympatric species, and as a by‐product of morphological evolution or geographical patterns. Here, we evaluate these hypotheses using closely related species pairs (sister taxa). We characterized the climatic niches of island endemic species and their closest relatives and calculated two metrics of niche divergence between the species (niche overlap and centroid distance). We compared these metrics between island endemics that have island‐dwelling sister taxa and those that have mainland‐dwelling sister taxa. We then related the degree of niche divergence to phylogenetic relatedness between the sister taxa, sympatry, morphological trait differences and island characteristics (isolation, size, age). Overall, despite significant niche divergence across species pairs, we found little evidence that competition or biotic interactions drive large‐scale climatic niche evolution in island mammals. Niche divergence in island‐endemic mammals is not driven by sympatry with their closest relatives, nor is it linked to phylogenetic relatedness. Furthermore, the phenotypic evolution of island‐endemic species does not lead to corresponding evolution in climatic niches. Instead, abiotic, geographical patterns appear to drive niche divergence in these species. Sister taxa that were more geographically isolated from each other had significantly lower niche overlaps. Island‐endemic mammals that live in montane regions likewise diverged from their closest relatives. These results suggest that competition between related species on islands may lead to niche partitioning only on local scales and that niche evolution in island‐endemic mammals may occur primarily in response to geographical patterns.