Old-growth forests are of high habitat value for many forest-dwelling species and of high cultural value for society. In areas with a long history of human land-use, such as in Central Europe, few old-growth forests remain, located predominately in protected areas such as national parks and wilderness areas. Protected areas safeguard old-growth forests against human land use, but not against the impacts of anthropogenic climate change. Using simulation-based scenario analyses we here assessed the development of old-growth in the 21st century, using a national park in the Northern Alps as example. Under climate change, old-growth decreased by up to 21% relative to simulations under baseline climate, with decreasing size and cohesion of old-growth patches on the landscape. Climate-mediated increases in disturbance were driving the decline in old-growth forests, with a near complete loss in old-growth beyond disturbance rates of 1.5% yr⁻¹. Conversely, structurally complex forests increased with disturbance, suggesting a decoupling of forest structure and demography in the 21st century. We conclude that climate change presents an indirect anthropogenic threat to old-growth forests in protected areas. Our findings highlight that climate impacts need to be considered explicitly in conservation planning, in order not to overestimate the effectiveness of protected areas.