Maintaining the diversity of wild bees is a priority for preserving ecosystem function and promoting stability and productivity of agroecosystems. However, wild bee communities face many threats and beekeeping could be one of them, because honey bees may have a strong potential to outcompete wild pollinators when placed at high densities. Yet, we still know little about how beekeeping intensity affects wild bee diversity and their pollinator interactions. Here, we explore how honey bee density relates to wild bee diversity and the structure of their pollination networks in 41 sites on 13 Cycladic Islands (Greece) with similar landscapes but differing in beekeeping intensity. Our large-scale study shows that increasing honey bee visitation rate had a negative effect on wild bee species richness and abundance, although the latter effect was relatively weak compared to the effect of other landscape variables. Competition for flowering resources (as indicated by a resource sharing index) increased with the abundance of honey bees, but the effect was more moderate for wild bees in family Apidae than for bees in other families, suggesting a stronger niche segregation in Apidae in response to honey bees. Honey bees also influenced the structure of wild bee pollination networks indirectly, through changes in wild bee richness. Low richness of wild bees in sites with high honey bee abundance resulted in wild bee networks with fewer links and lower linkage density. Our results warn against beekeeping intensification in these islands and similar hotspots of bee diversity, and shed light on how benefits to pollination services of introducing honey bees may be counterbalanced by detriments to wild bees and their ecosystem services.