DNA double-strand breaks (DSBs) pose a severe challenge to genomic integrity. While various repair pathways exist, only homologous recombination ensures error-free repair by restoring missing information through physical interactions with a homologous region in the genome. In somatic cells, homologous recombination is much more efficient between sister chromatids of replicated chromosomes than between homologous copies of a chromosome, suggesting that homology search might be facilitated by the 3D organization of sister chromatids. To investigate the role of chromosome organization in DNA repair, we developed sister-chromatid-sensitive conformation capture methods, using high-throughput sequencing (scsHi-C) and programmable multiplexed in situ hybridization (scsFISH). Using these methods, we show that broken DNA ends scan a megabase-sized domain on the opposing sister chromatid. We find that cohesin regulates the homology scanning process both through its loop-extruding as well as its cohesive functions. Our study hence reveals how the 3D organization of replicated chromosomes contributes to DNA repair.