Polymer vesicles, commonly referred to as polymersomes, are self-organized materials that result from the self-assembly of amphiphilic copolymers in solution. Recently, there has been increasing interest in biomedical applications of polymersomes due to the different functions that can be imparted through encapsulation of molecules within the core or membrane or through the introduction of bioactive molecules to the polymersome surface. We describe here the development and study of poly(ethylene oxide)-polycaprolactone polymersomes designed to interact with influenza viruses at two different stages in the infection process. First, the conjugation of the sialic acid N-acetylneuraminic acid (Neu5Ac) to the polymersome surface was designed to inhibit the binding of viral hemagglutinin to sialic acids on host cells, thus preventing viral entry. Second, the incorporation of the neuraminidase inhibitor zanamivir into the polymersome core was designed to prevent the release of progeny virus from the host cells, thus inhibiting viral replication. With the aim of maximizing multivalent effects at the polymersome surface, polyester dendrons functionalized with Neu5Ac were synthesized and conjugated to polymersomes. Binding of the resulting dendritic sialopolymersomes to Limax flavus agglutinin was studied and compared to the sialodendron and a monovalent Neu5Ac derivative using an enzyme-linked lectin inhibition assay. It was found that while the sialodendron exhibited a 17-fold enhancement (per sialoside) relative to the small molecule, the dendritic sialopolymersomes resulted in an almost 2000-fold enhancement in binding affinity. It was also demonstrated that encapsulation of zanamivir into the dendritic sialopolymersomes could be performed with the same efficiency as for naked polymersomes to provide a drug loading of ~35 wt %. Drug release rates were similar for both systems with sustained release over a period of 4 days. Overall, these results suggest the promise of using a multifunctional polymersome system for interaction with and inhibition of influenza viruses.