The foraging behaviour of species determines their diet and, therefore, also emergent food-web structure. Optimal foraging theory (OFT) has previously been applied to understand the emergence of food-web structure through a consumer-centric consideration of diet choice. However, the resource-centric viewpoint, where species adjust their behaviour to reduce the risk of predation, has not been considered. We develop a mechanistic model that merges metabolic theory with OFT to incorporate the effect of predation risk on diet choice to assemble food webs. This 'predation-risk-compromise' (PR) model better captures the nestedness and modularity of empirical food webs relative to the classical optimal foraging model. Specifically, compared with optimal foraging alone, risk-mitigated foraging leads to more-nested but less-modular webs by broadening the diet of consumers at intermediate trophic levels. Thus, predation risk significantly affects food-web structure by constraining species' ability to forage optimally, and needs to be considered in future work.