Most practical materials are held together by covalent bonds, which are irreversible. Materials based on noncovalent interactions can undergo reversible self-assembly, which offers advantages in terms of fabrication, processing and recyclability(1), but the majority of noncovalent systems are too fragile to be competitive with covalent materials for practical applications, despite significant attempts to develop robust noncovalent arrays(1-4). Here, we report nanostructured supramolecular membranes prepared from fibrous assemblies(5) in water. The membranes are robust due to strong hydrophobic interactions(6,7), allowing their application in the size-selective separation of both metal and semiconductor nanoparticles. A thin (12 mu m) membrane is used for filtration (similar to 5 nm cutoff), and a thicker (45 mu m) membrane allows for size-selective chromatography in the sub-5 nm domain. Unlike conventional membranes, our supramolecular membranes can be disassembled using organic solvent, cleaned, reassembled and reused multiple times.