Organisms must carefully control their metabolism in order to survive. On the other hand, enzymes must adapt in response to evolutionary pressures on the pathways in which they are imbedded. Taking advantage of the newly available whole-genome sequences of 12 Drosophila species, we examined how protein function and metabolic network architecture influence rates of enzyme evolution. We found that despite high overall constraint, there were significant differences in rates of amino acid substitution among functional classes of enzymes. This heterogeneity arises because proteins involved in the metabolism of foreign compounds evolve relatively rapidly, whereas enzymes that act in “core” metabolism exhibit much slower rates of amino acid replacement, suggesting strong selective constraint. Network architecture also influences enzymes’ rates of amino acid replacement. In particular, enzymes that share metabolites with many other enzymes are relatively constrained, although apparently not because they are more likely to be essential. Our analyses suggest that this pattern is driven by strong constraint of enzymes acting at branch points in metabolic pathways. We conclude that metabolic network architecture and enzyme function separately affect enzyme evolution rates.