The organization of biological materials into versatile three-dimensional assemblies could be used to build multifunctional therapeutic scaffolds for use in nanomedicine. Here, we report a strategy to design three-dimensional nanoscale scaffolds that can be self-assembled from RNA with precise control over their shape, size and composition. These cubic nanoscaffolds are only ∼13 nm in diameter and are composed of short oligonucleotides, making them amenable to chemical synthesis, point modifications and further functionalization. Nanocube assembly is verified by gel assays, dynamic light scattering and cryogenic electron microscopy. Formation of functional RNA nanocubes is also demonstrated by incorporation of a light-up fluorescent RNA aptamer that is optimally active only upon full RNA assembly. Moreover, we show that the RNA nanoscaffolds can self-assemble in isothermal conditions (37 °C) during in vitro transcription, which opens a route towards the construction of sensors, programmable packaging and cargo delivery systems for biomedical applications.