Chemistry plays a crucial role in creating synthetic analogues of biomacromolecular structures. Of particular scientific and technological interest are biomimetic vesicles that are inspired by natural membrane compartments and organelles but avoid their drawbacks, such as membrane instability and limited control over cargo transport across the boundaries. In this study, completely synthetic vesicles were developed from stable polymeric walls and easy-to-engineer membrane DNA nanopores. The hybrid nanocontainers feature selective permeability and permit the transport of organic molecules of 1.5 nm size. Larger enzymes (ca. 5 nm) can be encapsulated and retained within the vesicles yet remain catalytically active. The hybrid structures constitute a new type of enzymatic nanoreactor. The high tunability of the polymeric vesicles and DNA pores will be key in tailoring the nanocontainers for applications in drug delivery, bioimaging, biocatalysis, and cell mimicry.