The catalytic cycle involves internal motions and conformational changes that allow enzymes to specifically bind to substrates, reach the transition state and release the product. Such mechanical interactions and motions are often long ranged so that mutations of residues far from the active site can modulate the enzymatic cycle. In particular, regions that undergo high strain during the cycle give mechanical flexibility to the protein, which is crucial for protein motion. Here we directly probe the connection between strain, flexibility and functionality, and we quantify how distant high-strain residues modulate the catalytic function via long-ranged force transduction. We measure the rheological and catalytic properties of wild-type guanylate kinase and of its mutants with a single amino acid replacement in low-/high-strain regions and in binding/non-binding regions. The rheological response of the protein to an applied oscillating force fits a continuum model of a viscoelastic material whose mechanical properties are significantly affected by mutations in high-strain regions, as opposed to mutations in control regions. Furthermore, catalytic activity assays show that mutations in high-strain or binding regions tend to reduce activity, whereas mutations in low-strain, non-binding regions are neutral. These findings suggest that enzymes act as viscoelastic catalytic machines with sequence-encoded mechanical specifications.