DNA double-strand breaks (DSBs) trigger specialized cellular mechanisms that collectively form the DNA damage response (DDR). In proliferating cells, the DDR serves the function of mending DNA breaks and satisfying the cell-cycle checkpoints. Distinct goals exist in differentiated cells that are postmitotic and do not face cell-cycle checkpoints. Nonetheless, the distinctive requirements and mechanistic details of the DDR in differentiated cells are still poorly understood. In this study, we set an in vitro differentiation model of human skeletal muscle myoblasts into multinucleated myotubes that allowed monitoring DDR dynamics during cell differentiation. Our results demonstrate that myotubes have a prolonged DDR, which is nonetheless competent to repair DSBs and render them significantly more resistant to cell death than their progenitors. Using live-cell microscopy and single-molecule kinetic measurements of transcriptional activity, we observed that myotubes respond to DNA damage by rapidly and transiently suppressing global gene expression and rewiring the epigenetic landscape of the damaged nucleus. Our findings provide novel insights into the DDR dynamics during cellular differentiation and shed light on the strategy employed by human skeletal muscle to preserve the integrity of the genetic information and sustain long-term organ function after DNA damage.