In Saccharomyces cerevisiae, histone H3 lysine 56 acetylation (H3K56ac) is a modification of new H3 molecules deposited throughout the genome during S-phase. H3K56ac is removed by the sirtuins Hst3 and Hst4 at later stages of the cell cycle. Previous studies indicated that regulated degradation of Hst3 plays an important role in the genome-wide waves of H3K56 acetylation and deacetylation that occur during each cell cycle. However, little is known regarding the mechanism of cell cycle-regulated Hst3 degradation. Here, we demonstrate that Hst3 instability in vivo is dependent upon the ubiquitin ligase SCF(Cdc4) and that Hst3 is phosphorylated at two Cdk1 sites, threonine 380 and threonine 384. This creates a diphosphorylated degron that is necessary for Hst3 polyubiquitylation by SCF(Cdc4). Mutation of the Hst3 diphospho-degron does not completely stabilize Hst3 in vivo, but it nonetheless results in a significant fitness defect that is particularly severe in mutant cells treated with the alkylating agent methyl methanesulfonate. Unexpectedly, we show that Hst3 can be degraded between G2 and anaphase, a window of the cell cycle where Hst3 normally mediates genome-wide deacetylation of H3K56. Our results suggest an intricate coordination between Hst3 synthesis, genome-wide H3K56 deacetylation by Hst3, and cell cycle-regulated degradation of Hst3 by cyclin-dependent kinases and SCF(Cdc4).