Cancers arise through the accumulation of genetic and epigenetic alterations that enable cells to evade telomere-based proliferative barriers and achieve immortality. One such barrier is replicative crisis—an autophagy-dependent program that eliminates checkpoint-deficient cells with unstable telomeres and other cancer-relevant chromosomal aberrations1,2. However, little is known about the molecular events that regulate the onset of this important tumour-suppressive barrier. Here we identified the innate immune sensor Z-DNA binding protein 1 (ZBP1) as a regulator of the crisis program. A crisis-associated isoform of ZBP1 is induced by the cGAS–STING DNA-sensing pathway, but reaches full activation only when associated with telomeric-repeat-containing RNA (TERRA) transcripts that are synthesized from dysfunctional telomeres. TERRA-bound ZBP1 oligomerizes into filaments on the outer mitochondrial membrane of a subset of mitochondria, where it activates the innate immune adapter protein mitochondrial antiviral-signalling protein (MAVS). We propose that these oligomerization properties of ZBP1 serve as a signal amplification mechanism, where few TERRA–ZBP1 interactions are sufficient to launch a detrimental MAVS-dependent interferon response. Our study reveals a mechanism for telomere-mediated tumour suppression, whereby dysfunctional telomeres activate innate immune responses through mitochondrial TERRA–ZBP1 complexes to eliminate cells destined for neoplastic transformation.