Diffusion of regulatory molecules during an enzymic reaction in micrometer and submicrometer reaction volumes can lead to mixing and transport times much shorter than the turnover time of enzymes. Our theoretical investigations of a stochastic model of an allosterically product-inhibited enzymic reaction show that under these conditions the turnover cycles of individual enzymes can become synchronized. Interactions between different enzymes realized by means of fast moving inhibitor molecules are responsible for such mutual synchronization. This synchronization is accompanied by rapid oscillations in the concentration of the reaction product.