On a global scale, fisheries harvest an estimated 96 million tonnes of fish biomass annually, making them one of the most important drivers of marine ecosystem biodiversity. Yet little is known about the interactions between fisheries and the dynamics of complex food webs in which the harvested species are embedded. We have developed a synthetic model that combines resource economics with complex food webs to examine the direct effects of fishing on exploited species and the indirect impact on other species in the same community. Our model analyses show that the sensitivity of the targeted species increases with its trophic level and decreases with its local interaction complexity (i.e. its number of interactions with prey, predators, and competitors). In addition, we also document a strikingly positive effect of community species richness on the resilience of the harvested species to this disturbance. The indirect effects on other species show specific patterns of spreading across trophic modules that differ systematically from how other disturbances spread across ecological networks. While these results call for further research on how human resource exploitation in general and fishery in particular affect ecological dynamics and biodiversity in naturally complex systems, they also allow for some cautious conclusions. Taken together, our results suggest that the sustainability concerning fishery yield and ecosystem integrity can be maximised by focusing the harvest on low trophic level species with a high local interaction complexity in high biodiversity ecosystems. In this sense, our complex network approach offers a promising avenue for integrating the necessities of generating economic revenue with the protection of natural biodiversity.