Many diseases are caused by failures of metabolic enzymes. These enzymes exist in the context of networks defined by the static topology of enzyme-metabolite interactions and by the reaction fluxes that are feasible at steady state. We use the local topology and the flux correlations to identify how failures in the metabolic network may lead to disease. First, using yeast as a model, we show that flux correlations are a powerful predictor of pairwise mutations that lead to cell death -- more powerful, in fact, than computational models that directly estimate the effects of mutations on cell fitness. These flux correlations, which can exist between enzymes far-separated in the metabolic network, add information to the structural correlations evident from shared metabolites. Second, we show that flux correlations in human align with similarities in Mendelian phenotypes ascribed to known genes. These methods will be useful in predicting genetic interactions in model organisms and understanding the combinatorial effects of genetic variations in humans.