Transcriptional heterogeneity due to plasticity of the epigenetic state of chromatin contributes to tumour evolution, metastasis and drug resistance1–3. However, the mechanisms that cause this epigenetic variation are incompletely understood. Here we identify micronuclei and chromosome bridges, aberrations in the nucleus common in cancer4,5, as sources of heritable transcriptional suppression. Using a combination of approaches, including long-term live-cell imaging and same-cell single-cell RNA sequencing (Look-Seq2), we identified reductions in gene expression in chromosomes from micronuclei. With heterogeneous penetrance, these changes in gene expression can be heritable even after the chromosome from the micronucleus has been re-incorporated into a normal daughter cell nucleus. Concomitantly, micronuclear chromosomes acquire aberrant epigenetic chromatin marks. These defects may persist as variably reduced chromatin accessibility and reduced gene expression after clonal expansion from single cells. Persistent transcriptional repression is strongly associated with, and may be explained by, markedly long-lived DNA damage. Epigenetic alterations in transcription may therefore be inherently coupled to chromosomal instability and aberrations in nuclear architecture.