Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio Rs, the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing Rs, the encounter rate is substantially depressed and becomes even nonmonotonic for Rs1. Concurrently with the saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction. © 2010 The American Physical Society.