In most theories of diffusion-influenced reactions, the reaction system is assumed to consist of a central reactant molecule surrounded by the other reactant molecules that pass each other freely. That is, excluded volumes among the like reactant molecules are neglected. We use the many-particle kernel formalism to investigate the effect of excluded volumes on the diffusion-influenced reaction. We obtain approximate analytic expressions for the many-particle kernel and the time profile of the survival probability of reactant molecules. The result is shown to be in good agreement with the Brownian dynamics simulation.