Influenza A virus (IAV) is a lytic RNA virus that triggers receptor-interacting serine/threonine-protein kinase 3 (RIPK3)-mediated pathways of apoptosis and mixed lineage kinase domain-like pseudokinase (MLKL)-dependent necroptosis in infected cells. ZBP1 initiates RIPK3-driven cell death by sensing IAV RNA and activating RIPK3. Here, we show that replicating IAV generates Z-RNAs, which activate ZBP1 in the nucleus of infected cells. ZBP1 then initiates RIPK3-mediated MLKL activation in the nucleus, resulting in nuclear envelope disruption, leakage of DNA into the cytosol, and eventual necroptosis. Cell death induced by nuclear MLKL was a potent activator of neutrophils, a cell type known to drive inflammatory pathology in virulent IAV disease. Consequently, MLKL-deficient mice manifest reduced nuclear disruption of lung epithelia, decreased neutrophil recruitment into infected lungs, and increased survival following a lethal dose of IAV. These results implicate Z-RNA as a new pathogen-associated molecular pattern and describe a ZBP1-initiated nucleus-to-plasma membrane "inside-out" death pathway with potentially pathogenic consequences in severe cases of influenza.