Eukaryotic cells have quality control systems that eliminate nonfunctional rRNAs with deleterious mutations (nonfunctional rRNA decay, NRD). We have previously reported that 25S NRD requires an E3 ubiquitin ligase complex, which is involved in ribosomal ubiquitination. However, the degradation process of nonfunctional ribosomes has remained unknown. Here, using genetic screening, we identified two ubiquitin-binding complexes, the Cdc48-Npl4-Ufd1 complex (Cdc48 complex) and the proteasome, as the factors involved in 25S NRD. We show that the nonfunctional 60S subunit is dissociated from the 40S subunit in a Cdc48 complex-dependent manner, before it is attacked by the proteasome. When we examined the nonfunctional 60S subunits that accumulated under proteasome-depleted conditions, the majority of mutant 25S rRNAs retained their full length at a single-nucleotide resolution. This indicates that the proteasome is an essential factor triggering rRNA degradation. We further showed that ribosomal ubiquitination can be stimulated solely by the suppression of the proteasome, suggesting that ubiquitin-proteasome-dependent RNA degradation occurs in broader situations, including in general rRNA turnover.