The high Arctic has the world's simplest terrestrial vertebrate predator–prey community, with the collared lemming being the single main prey of four predators, the snowy owl, the Arctic fox, the long-tailed skua, and the stoat. Using a 20-year-long time series of population densities for the five species and a dynamic model that has been previously parameterized for northeast Greenland, we analyzed the population and community level consequences of the ongoing and predicted climate change. Species' responses to climate change are complex, because in addition to the direct effects of climate change, which vary depending on species' life histories, species are also affected indirectly due to, e.g., predator–prey interactions. The lemming–predator community exemplifies these complications, yet a robust conclusion emerges from our modeling: in practically all likely scenarios of how climate change may influence the demography of the species, climate change increases the length of the lemming population cycle and decreases the maximum population densities. The latter change in particular is detrimental to the populations of the predators, which are adapted to make use of the years of the greatest prey abundance. Therefore, climate change will indirectly reduce the predators' reproductive success and population densities, and may ultimately lead to local extinction of some of the predator species. Based on these results, we conclude that the recent anomalous observations about lack of cyclic lemming dynamics in eastern Greenland may well be the first signs of a severe impact of climate change on the lemming–predator communities in Greenland and elsewhere in the high Arctic.