Viral pathogens are an ongoing threat to public health worldwide. Analysing their dependence on host biosynthetic pathways could lead to effective antiviral therapies1. Here we integrate proteomic analyses of polysomes with functional genomics and pharmacological interventions to define how enteroviruses and flaviviruses remodel host polysomes to synthesize viral proteins and disable host protein production. We find that infection with polio, dengue or Zika virus markedly modifies polysome composition, without major changes to core ribosome stoichiometry. These viruses use different strategies to evict a common set of translation initiation and RNA surveillance factors from polysomes while recruiting host machineries that are specifically required for viral biogenesis. Targeting these specialized viral polysomes could provide a new approach for antiviral interventions. For example, we find that both Zika and dengue use the collagen proline hydroxylation machinery to mediate cotranslational modification of conserved proline residues in the viral polyprotein. Genetic or pharmacological inhibition of proline hydroxylation impairs nascent viral polyprotein folding and induces its aggregation and degradation. Notably, such interventions prevent viral polysome remodelling and lower virus production. Our findings delineate the modular nature of polysome specialization at the virus-host interface and establish a powerful strategy to identify targets for selective antiviral interventions.