Several epithelial tissues contain stem cell reserves to replenish cells lost during normal homeostasis or upon injury. However, how epithelial tissues respond to distinct types of damage, and how stem cell plasticity and proliferation are regulated in these contexts, remain poorly understood. Here, we reveal that genotoxic agents, but not mechanical damage, induce hyperplasia and lineage infidelity in three related epithelial tissues: the mammary gland, interfollicular epidermis and hair follicle. Furthermore, DNA damage also promotes stromal proliferation. In the mammary gland, we find that DNA damage activates multipotency within the myoepithelial population and hyper-proliferation of their luminal progeny, resulting in tissue disorganization. Additionally, in epidermal and hair follicle epithelia, DNA damage induces basal cell hyperplasia with the formation of abnormal, multi-layered K14+/K10+ cells.This behavior does not involve apoptosis or immunity, and is epithelial cell non-autonomous; stromal fibroblasts are both necessary and sufficient to induce the epithelial response. Thus, genotoxic agents that are used chemotherapeutically to promote cancer cell death can have the opposite effect on wildtype epithelial tissue, paradoxically promoting hyperplasia and inducing both stemness and lineage infidelity.