The proteasome is a major proteolytic machine that regulates cellular proteostasis through selective degradation of ubiquitylated proteins1,2. A number of ubiquitin-related molecules have recently been found to be involved in the regulation of biomolecular condensates or membraneless organelles, which arise by liquid-liquid phase separation of specific biomolecules, including stress granules, nuclear speckles and autophagosomes3-8, but it remains unclear whether the proteasome also participates in such regulation. Here we reveal that proteasome-containing nuclear foci form under acute hyperosmotic stress. These foci are transient structures that contain ubiquitylated proteins, p97 (also known as valosin-containing protein (VCP)) and multiple proteasome-interacting proteins, which collectively constitute a proteolytic centre. The major substrates for degradation by these foci were ribosomal proteins that failed to properly assemble. Notably, the proteasome foci exhibited properties of liquid droplets. RAD23B, a substrate-shuttling factor for the proteasome, and ubiquitylated proteins were necessary for formation of proteasome foci. In mechanistic terms, a liquid-liquid phase separation was triggered by multivalent interactions of two ubiquitin-associated domains of RAD23B and ubiquitin chains consisting of four or more ubiquitin molecules. Collectively, our results suggest that ubiquitin-chain-dependent phase separation induces the formation of a nuclear proteolytic compartment that promotes proteasomal degradation.