Sulfolobus acidocaldarius is the closest experimentally tractable archaeal relative of eukaryotes and, despite lacking obvious cyclin-dependent kinase and cyclin homologs, has an ordered eukaryote-like cell cycle with distinct phases of DNA replication and division. Here, in exploring the mechanism of cell division in S. acidocaldarius, we identify a role for the archaeal proteasome in regulating the transition from the end of one cell cycle to the beginning of the next. Further, we identify the archaeal ESCRT-III homolog, CdvB, as a key target of the proteasome and show that its degradation triggers division by allowing constriction of the CdvB1:CdvB2 ESCRT-III division ring. These findings offer a minimal mechanism for ESCRT-III-mediated membrane remodeling and point to a conserved role for the proteasome in eukaryotic and archaeal cell cycle control.