Stem cells in plants constantly supply daughter cells to form new organs and are expected to safeguard the integrity of the cells from biological invasion. Here, we show how stem cells of the Arabidopsis shoot apical meristem and their nascent daughter cells suppress infection by cucumber mosaic virus (CMV). The stem cell regulator WUSCHEL responds to CMV infection and represses virus accumulation in the meristem central and peripheral zones. WUSCHEL inhibits viral protein synthesis by repressing the expression of plant S-adenosyl-L-methionine-dependent methyltransferases, which are involved in ribosomal RNA processing and ribosome stability. Our results reveal a conserved strategy in plants to protect stem cells against viral intrusion and provide a molecular basis for WUSCHEL-mediated broad-spectrum innate antiviral immunity in plants.