Proliferating cells coordinate histone and DNA synthesis to maintain correct stoichiometry for chromatin assembly. Histone mRNA levels must be repressed when DNA replication is inhibited to prevent toxicity and genome instability due to free non-chromatinized histone proteins. In mammalian cells, replication stress triggers degradation of histone mRNAs, but it is unclear if this mechanism is conserved from other species. The aim of this study was to identify the histone mRNA decay pathway in the yeast Saccharomyces cerevisiae and determine the mechanism by which DNA replication stress represses histone mRNAs. Using reverse transcription-quantitative PCR and chromatin immunoprecipitation–quantitative PCR, we show here that histone mRNAs can be degraded by both 5′ → 3′ and 3′ → 5′ pathways; however, replication stress does not trigger decay of histone mRNA in yeast. Rather, replication stress inhibits transcription of histone genes by removing the histone gene–specific transcription factors Spt10p and Spt21p from histone promoters, leading to disassembly of the preinitiation complexes and eviction of RNA Pol II from histone genes by a mechanism facilitated by checkpoint kinase Rad53p and histone chaperone Asf1p. In contrast, replication stress does not remove SCB-binding factor transcription complex, another activator of histone genes, from the histone promoters, suggesting that Spt10p and Spt21p have unique roles in the transcriptional downregulation of histone genes during replication stress. Together, our data show that, unlike in mammalian cells, replication stress in yeast does not trigger decay of histone mRNAs but inhibits histone transcription.