Aurora B regulates cytokinesis timing and plays a central role in the abscission checkpoint. Cellular events monitored by this checkpoint are beginning to be elucidated, yet signaling pathways upstream of Aurora B in this context remain poorly understood. Here we reveal a new connection between postmitotic genome surveillance and cytokinetic abscission. Underreplicated DNA lesions are known to be transmitted through mitosis and protected in newly formed nuclei by recruitment of 53BP1 and other proteins until repair takes place. We find that this genome surveillance initiates before completion of cytokinesis. Elevating replication stress increases this postmitotic process and delays cytokinetic abscission by keeping the abscission checkpoint active. We further find that ATR activity in midbody-stage cells links postmitotic genome surveillance to abscission timing and that Chk1 integrates this and other signals upstream of Aurora B to regulate when the final step in the physical separation of daughter cells occurs.