Stress granules (SGs) are conserved biomolecular condensates that originate in response to many stress conditions. These membraneless organelles contain nontranslating mRNAs and a diverse subproteome, but our knowledge of their regulation and functional relevance is still incipient. Here, we describe a mutual-inhibition interplay between SGs and Cdc28, the budding yeast Cdk. Among Cdc28 interactors acting as negative modulators of Start, we have identified Whi8, an RNA-binding protein that localizes to SGs and recruits the mRNA of CLN3, the most upstream G1 cyclin, for efficient translation inhibition and Cdk inactivation under stress. However, Whi8 also contributes to recruiting Cdc28 to SGs, where it acts to promote their dissolution. As predicted by a mutual-inhibition framework, the SG constitutes a bistable system that is modulated by Cdk. Since mammalian cells display a homologous mechanism, we propose that the opposing functions of specific mRNA-binding proteins and Cdk’s subjugate SG dynamics to a conserved hysteretic switch.