Disease risk is a potential cost of group living. Although modular organization is thought to reduce this cost in animal societies, empirical evidence toward this hypothesis has been conflicting. We analyzed empirical social networks from 43 animal species to motivate our study of the epidemiological consequences of modular structure in animal societies. From these empirical studies, we identified the features of interaction patterns associated with network modularity and developed a theoretical network model to investigate when and how subdivisions in social networks influence disease dynamics. Contrary to prior work, we found that disease risk is largely unaffected by modular structure, although social networks beyond a modular threshold experience smaller disease burden and longer disease duration. Our results illustrate that the lowering of disease burden in highly modular social networks is driven by two mechanisms of modular organization: network fragmentation and subgroup cohesion. Highly fragmented social networks with cohesive subgroups are able to structurally trap infections within a few subgroups and also cause a structural delay to the spread of disease outbreaks. Finally, we show that network models incorporating modular structure are necessary only when prior knowledge suggests that interactions within the population are highly subdivided. Otherwise, null networks based on basic knowledge about group size and local contact heterogeneity may be sufficient when data-limited estimates of epidemic consequences are necessary. Overall, our work does not support the hypothesis that modular structure universally mitigates the disease impact of group living.