More than half of disease-causing missense variants are thought to lead to protein degradation, but the molecular mechanism of how these variants are recognized by the cell remains enigmatic. Degrons are stretches of amino acids that help mediate recognition by E3 ligases and thus confer protein degradation via the ubiquitin-proteasome system. While degrons that mediate controlled degradation of, for example, signaling components and cell-cycle regulators are well described, so-called protein-quality-control degrons that mediate the degradation of destabilized proteins are poorly understood. Here, we show that disease-linked dihydrofolate reductase (DHFR) missense variants are structurally destabilized and chaperone-dependent proteasome targets. We find two regions in DHFR that act as degrons, and the proteasomal turnover of one of these was dependent on the molecular chaperone Hsp70. Structural analyses by nuclear magnetic resonance (NMR) and hydrogen/deuterium exchange revealed that this degron is buried in wild-type DHFR but becomes transiently exposed in the disease-linked missense variants.