In hydrogenases and many other redox enzymes, the buried active site is connected to the solvent by a molecular channel whose structure may determine the enzyme's selectivity with respect to substrate and inhibitors. The role of these channels has been addressed using crystallography and molecular dynamics, but kinetic data are scarce. Using protein film voltammetry, we determined and then compared the rates of inhibition by CO and O2 in ten NiFe hydrogenase mutants and two FeFe hydrogenases. We found that the rate of inhibition by CO is a good proxy of the rate of diffusion of O2 toward the active site. Modifying amino acids whose side chains point inside the tunnel can slow this rate by orders of magnitude. We quantitatively define the relations between diffusion, the Michaelis constant for H2 and rates of inhibition, and we demonstrate that certain enzymes are slowly inactivated by O2 because access to the active site is slow.