The growing apices of plants contain stem cells that continually produce tissues, which, in the shoot, include the germline. These stem cell populations remain active throughout the plant's life, which can last for centuries, and are particularly exposed to environmental hazards that cause DNA damage and mutations. It is not known whether plants have mechanisms to safeguard the genome specifically in these crucial cell populations. Here, we show that root and shoot stem cells and their early descendants are selectively killed by mild treatment with radiomimetic drugs, x-rays, or mutations that disrupt DNA repair by nonhomologous end-joining. Stem cell death required transduction of DNA damage signals by the ATAXIA-TELANGIECTASIA MUTATED (ATM) kinase and, specifically in the root, also the ATM/RAD3-RELATED (ATR) kinase. Consistent with the absence of p53 and the core apoptotic machinery in plants, death of the stem cells did not show apoptotic but autolytic features as seen in other cases of plant developmentally programmed cell death. We propose that plants have independently evolved selective death as a stringent mechanism to safeguard genome integrity in their stem cell populations.