Microscopic simulations based on a direct simulation Monte Carlo method are performed to generate a reaction-diffusion wave front for reactions with or without activation energy. For fast reactions, the mean propagation speed of the front and its profile width differ from their predictions obtained from the standard reaction-diffusion equation. These discrepancies are related to the perturbation of equilibrium particle velocity distribution. To improve the analytical prediction of macroscopic front properties, we deduce from the Boltzmann equation the corrections to the macroscopic equation governing the evolution of concentrations of chemical species. In addition to these nonequilibrium effects, the discreteness of particle populations in the simulations induces deviations from the continuous description.