Climate change is one of the most influential drivers of biodiversity. Species-specific differences in the reaction to climate change can become particularly important when interacting species are considered. Current studies have evidenced temporal mismatching of interacting species at single points in space, and recently two investigations showed that species interactions are relevant for their future ranges. However, so far we are not aware that the ranges of interacting species may become substantially spatially mismatched. We developed separate ecological-niche models for a monophagous butterfly (Boloria titania) and its larval host plant (Polygonum bistorta) based on monthly interpolated climate data, land-cover classes, and soil data at a 10'-grid resolution. We show that all of three chosen global-change scenarios, which cover a broad range of potential developments in demography, socio-economics, and technology during the 21st century from moderate to intermediate to maximum change, will result in a pronounced spatial mismatch between future niche spaces of these species. The butterfly may expand considerably its future range (by 124-258%) if the host plant has unlimited dispersal, but it could lose 52-75% of its current range if the host plant is not able to fill its projected ecological niche space, and 79-88% if the butterfly also is assumed to be highly dispersal limited. These findings strongly suggest that climate change has the potential to disrupt trophic interactions because co-occurring species do not necessarily react in a similar manner to global change, having important consequences at ecological and evolutionary time scales.