The kinetics of the peroxidase-catalyzed oxidation of iodide was found to be strongly nonlinear under certain conditions. At slightly acidic pH, the reaction behaves like an enzymatic "iodine clock", i.e., the reaction is switched on after a well-defined time depending on the initial concentrations of the reactants. This behavior is studied experimentally and is shown to represent a true dynamic enzymatic switch. Numerical simulations of a mechanistic model strengthen this conclusion.