The double-stranded RNA sensor kinase PKR is one of four integrated stress response (ISR) sensor kinases that phosphorylate the α subunit of eukaryotic initiation factor 2 (eIF2α) in response to stress. The current model of PKR activation considers the formation of back-to-back PKR dimers as a prerequisite for signal propagation. Here we show that PKR signaling involves the assembly of dynamic PKR clusters. PKR clustering is driven by ligand binding to PKR's sensor domain and by front-to-front interfaces between PKR's kinase domains. PKR clusters are discrete, heterogeneous, autonomous coalescences that share some protein components with processing bodies. Strikingly, eIF2α is not recruited to PKR clusters, and PKR cluster disruption enhances eIF2α phosphorylation. Together, these results support a model in which PKR clustering may limit encounters between PKR and eIF2α to buffer downstream signaling and prevent the ISR from misfiring.