Climate is a major factor delimiting species’ distributions. However, biotic interactions may also be prominent in shaping geographical ranges, especially for parapatric species forming hybrid zones. Determining the relative effect of each factor and their interaction of the contact zone location has been difficult due to the lack of broad scale environmental data. Recent developments in species distribution modelling (SDM) now allow disentangling the relative contributions of climate and species’ interactions in hybrid zones and their responses to future climate change. We investigated the moving hybrid zone between the breeding ranges of two parapatric passerines in Europe. We conducted SDMs representing the climatic conditions during the breeding season. Our results show a large mismatch between the realized and potential distributions of the two species, suggesting that interspecific interactions, not climate, account for the present location of the contact zone. The SDM scenarios show that the southerly distributed species, Hippolais polyglotta, might lose large parts of its southern distribution under climate change, but a similar gain of novel habitat along the hybrid zone seems unlikely, because interactions with the other species (H. icterina) constrain its range expansion. Thus, whenever biotic interactions limit range expansion, species may become ‘trapped’ if range loss due to climate change is faster than the movement of the contact zone. An increasing number of moving hybrid zones are being reported, but the proximate causes of movement often remain unclear. In a global context of climate change, we call for more interest in their interactions with climate change.