Alpine and Arctic species are considered to be particularly vulnerable to climate change, which is expected to cause habitat loss, fragmentation and—ultimately—extinction of cold-adapted species. However, the impact of climate change on glacial relict populations is not well understood, and specific recommendations for adaptive conservation management are lacking. We focused on the mountain hare (Lepus timidus) as a model species and modelled species distribution in combination with patch and landscape-based connectivity metrics. They were derived from graph-theory models to quantify changes in species distribution and to estimate the current and future importance of habitat patches for overall population connectivity. Models were calibrated based on 1,046 locations of species presence distributed across three biogeographic regions in the Swiss Alps and extrapolated according to two IPCC scenarios of climate change (RCP 4.5 & 8.5), each represented by three downscaled global climate models. The models predicted an average habitat loss of 35% (22%–55%) by 2100, mainly due to an increase in temperature during the reproductive season. An increase in habitat fragmentation was reflected in a 43% decrease in patch size, a 17% increase in the number of habitat patches and a 34% increase in inter-patch distance. However, the predicted changes in habitat availability and connectivity varied considerably between biogeographic regions: Whereas the greatest habitat losses with an increase in inter-patch distance were predicted at the southern and northern edges of the species’ Alpine distribution, the greatest increase in patch number and decrease in patch size is expected in the central Swiss Alps. Finally, both the number of isolated habitat patches and the number of patches crucial for maintaining the habitat network increased under the different variants of climate change. Focusing conservation action on the central Swiss Alps may help mitigate the predicted effects of climate change on population connectivity.