Influence of diffusion on the Michaelis-Menten kinetics is investigated with the renormalized kinetic theory recently proposed by Yang [J. Chem. Phys. 108, 117; 108, 8557; 108, 9069 (1998)]. The nonlinearity predicted previously by Zhou [J. Phys. Chem. 101, 6642 (1997)] in the Lineweaver-Burk plot for the high concentration of substrate with his empirical expression and simulation is correctly obtained by the kinetic theory. We discuss possible errors in the estimation of reaction parameters caused by ignoring this nonlinearity in an experimental analysis (performed at even lower concentrations of the substrate). The time evolution of the production rate shows a peak before it reaches the steady-state value. The long time asymptotic relaxation of the deviation of the enzyme concentration from the steady-state value shows t(-1/2) power-law behavior instead of the exponential decay predicted by the classical kinetics.