To efficiently duplicate their genomic content, cells must overcome DNA lesions that interfere with processive DNA replication. These lesions may be removed and repaired, rather than just tolerated, to allow continuity of DNA replication on an undamaged DNA template. However, it is unclear how this is achieved at a molecular level. Here we identify a new replication-associated factor, ZRANB3 (zinc finger, RAN-binding domain containing 3), and propose its role in the repair of replication-blocking lesions. ZRANB3 has a unique structure-specific endonuclease activity, which is coupled to ATP hydrolysis. It cleaves branched DNA structures with unusual polarity, generating an accessible 3'-OH group in the template of the leading strand. Furthermore, ZRANB3 localizes to DNA replication sites and interacts with the components of the replication machinery. It is recruited to damaged replication forks via multiple mechanisms, which involve interactions with PCNA, K63-polyubiquitin chains, and branched DNA structures. Collectively, our data support a role for ZRANB3 in the replication stress response and suggest new insights into how DNA repair is coordinated with DNA replication to maintain genome stability.