Exosomes secreted by irradiated cells mediate radiation-induced bystander effect, which is manifested by DNA breaks detected in recipient cells, yet the specific mechanism responsible for the generation of chromosome lesions remains unclear. In this study, naïve FaDu head and neck cancer cells were stimulated with exosomes released by irradiated (a single 2Gy dose) or mock-irradiated cells. Maximum accumulation of gamma H2A.X foci, a marker of DNA breaks, was detected after one hour of stimulation with exosomes from irradiated donors, which level was comparable to the one observed in directly irradiated cells. Exosomes from irradiated cells, but not from control ones, activated two stress-induced protein kinases ATM and ATR. Noteworthy, while direct irradiation activated only ATM, both ATM and ATR were activated by two factors known to induce the replication stress: hydroxyurea and camptothecin (with subsequent phosphorylation of gamma H2A.X). One hour of stimulation with exosomes from irradiated cells suppressed DNA synthesis in recipient cells and resulted in the subsequent nuclear accumulation of RNA:DNA hybrids, which is an indicator of impaired replication. Interestingly, the abovementioned effects were observed before a substantial internalization of exosomes, which may suggest a receptor-mediated mechanism. After one hour of stimulation with exosomes from irradiated donors increased phosphorylation of several nuclear proteins was observed, including replication factors and regulators of heterochromatin remodeling, as well as components of multiple intracellular signaling pathways. Moreover, analysis of gene and protein profiles of recipient cells performed after 24 hours of stimulation with exosomes from irradiated donors revealed that upregulated transcripts and proteins were associated with GO terms related to the regulation of DNA replication and cell division. Hence, we concluded that the bystander effect mediated by exosomes released from irradiated cells involves the replication stress in recipient cells. We hypothesize that this type of stress, depending on the specific cellular context, may have either cytotoxic or cytoprotective consequences for target cells.