Epistatic interactions, manifested in the effects of mutations on the phenotypes caused by other mutations, may help uncover the functional organization of complex biological networks. Here, we studied system-level epistatic interactions by computing growth phenotypes of all single and double knockouts of 890 metabolic genes in Saccharomyces cerevisiae, using the framework of flux balance analysis. A new scale for epistasis identified a distinctive trimodal distribution of these epistatic effects, allowing gene pairs to be classified as buffering, aggravating or noninteracting. We found that the ensuing epistatic interaction network could be organized hierarchically into function-enriched modules that interact with each other 'monochromatically' (i.e., with purely aggravating or purely buffering epistatic links). This property extends the concept of epistasis from single genes to functional units and provides a new definition of biological modularity, which emphasizes interactions between, rather than within, functional modules. Our approach can be used to infer functional gene modules from purely phenotypic epistasis measurements.