Nucleic acids are substrates for different types of damage, but little is known about the fate of damaged RNAs. We addressed the existence of an RNA-damage response in yeast. The decay kinetics of GAL1p-driven mRNAs revealed a dose-dependent mRNA stabilization upon UV-irradiation that was not observed after heat or saline shocks, or during nitrogen starvation. UV-induced mRNA stabilization did not depend on DNA repair, damage checkpoint or mRNA degradation machineries. Notably, fluorescent in situ hybridization revealed that after UV-irradiation, polyadenylated mRNA accumulated in cytoplasmic foci that increased in size with time. In situ colocalization showed that these foci are not processing-bodies, eIF4E-, eIF4G-, and Pab1-containing bodies, stress granules, autophagy vesicles, or part of the secretory or endocytic pathways. These results point to the existence of a specific eukaryotic RNA-damage response, which leads to new polyadenylated mRNA-containing granules (UV-induced mRNA granules; UVGs). We propose that potentially damaged mRNAs, which may be deleterious to the cell, are temporarily stored in UVG granules to safeguard cell viability.