Species across the planet are shifting their ranges to track suitable climate conditions in response to climate change. Given that protected areas have higher quality habitat and often harbor higher levels of biodiversity compared to unprotected lands, it is often assumed that protected areas can serve as steppingstones for species undergoing climate-induced range shifts. However, there are several factors that may impede successful range shifts among protected areas, including the distance that must be travelled, unfavorable human land uses and climate conditions along potential movement routes, and lack of analogous climates. Through a species-agnostic lens, we evaluate these factors across the global terrestrial protected area network as measures of climate connectivity, which is defined as the ability of a landscape to facilitate or impede climate-induced movement. We found that over half of protected land areas and two-thirds of the number of protected units across the globe are at risk of climate connectivity failure, casting doubt on whether many species can successfully undergo climate-induced range shifts among protected areas. Consequently, protected areas are unlikely to serve as steppingstones for a large number of species under a warming climate. As species disappear from protected areas without commensurate immigration of species suited to the emerging climate (due to climate connectivity failure), many protected areas may be left with a depauperate suite of species under climate change. Our findings are highly relevant given recent pledges to conserve 30% of the planet by 2030 (30x30), underscore the need for innovative land management strategies that allow for species range shifts, and suggest that assisted colonization may be necessary to promote species that are adapted to the emerging climate.