The mechanisms underlying chromosome segregation in prokaryotes remain a subject of debate and no unifying view has yet emerged. Given that the initial disentanglement of duplicated chromosomes could be achieved by purely entropic forces, even the requirement of an active prokaryotic segregation machinery has been questioned. Using computer simulations, we show that entropic forces alone are not sufficient to achieve and maintain full separation of chromosomes. This is, however, possible by assuming repeated binding of chromosomes along a gradient of membrane-associated tethering sites toward the poles. We propose that, in Escherichia coli, such a gradient of membrane tethering sites may be provided by the oscillatory Min system, otherwise known for its role in selecting the cell division site. Consistent with this hypothesis, we demonstrate that MinD binds to DNA and tethers it to the membrane in an ATP-dependent manner. Taken together, our combined theoretical and experimental results suggest the existence of a novel mechanism of chromosome segregation based on the Min system, further highlighting the importance of active segregation of chromosomes in prokaryotic cell biology.