DNA nanotechnology provides a versatile and powerful tool to dissect the structure-function relationship of biomolecular machines like the nuclear pore complex (NPC), an enormous protein assembly that controls molecular traffic between the nucleus and cytoplasm. To understand how the intrinsically disordered, Phe-Gly-rich nucleoporins (FG-nups) within the NPC establish a selective barrier to macromolecules, we built a DNA-origami NanoTrap. The NanoTrap comprises precisely arranged FG-nups in an NPC-like channel, which sits on a baseplate that captures macromolecules that pass through the FG network. Using this biomimetic construct, we determined that the FG-motif type, grafting density, and spatial arrangement are critical determinants of an effective diffusion barrier. Further, we observed that diffusion barriers formed with cohesive FG interactions dominate in mixed-FG-nup scenarios. Finally, we demonstrated that the nuclear transport receptor, Ntf2, can selectively transport model cargo through NanoTraps composed of FxFG but not GLFG Nups. Our NanoTrap thus recapitulates the NPC's fundamental biological activities, providing a valuable tool for studying nuclear transport.