The E. coli MinCDE system has become a paradigmatic reaction-diffusion system in biology. The membrane-bound ATPase MinD and ATPase-activating protein MinE oscillate between the cell poles followed by MinC, thus positioning the main division protein FtsZ at midcell. Here we report that these energy-consuming MinDE oscillations may play a role beyond constraining MinC/FtsZ localization. Using an in vitro reconstitution assay, we show that MinDE self-organization can spatially regulate a variety of functionally completely unrelated membrane proteins into patterns and gradients. By concentration waves sweeping over the membrane, they induce a direct net transport of tightly membrane-attached molecules. That the MinDE system can spatiotemporally control a much larger set of proteins than previously known, may constitute a MinC-independent pathway to division site selection and chromosome segregation. Moreover, the here described phenomenon of active transport through a traveling diffusion barrier may point to a general mechanism of spatiotemporal regulation in cells.