Mutation signatures associated with apolipoprotein B mRNA editing catalytic polypeptide-like 3A/B (APOBEC3A/B) cytidine deaminases are prevalent across cancers, implying their roles as mutagenic drivers during tumorigenesis and tumor evolution. APOBEC3A (A3A) expression induces DNA replication stress and increases the cellular dependency on the ataxia telangiectasia and Rad3-related (ATR) kinase for survival. Nonetheless, how A3A induces DNA replication stress remains unclear. We show that A3A induces replication stress without slowing replication forks. We find that A3A induces single-stranded DNA (ssDNA) gaps through PrimPol-mediated repriming. A3A-induced ssDNA gaps are repaired by multiple pathways involving ATR, RAD51, and translesion synthesis. Both ATR inhibition and trapping of poly(ADP-ribose) polymerase (PARP) on DNA by PARP inhibitor impair the repair of A3A-induced gaps, preferentially killing A3A-expressing cells. When used in combination, PARP and ATR inhibitors selectively kill A3A-expressing cells synergistically in a manner dependent on PrimPol-generated gaps. Thus, A3A-induced replication stress arises from PrimPol-generated ssDNA gaps, which confer a therapeutic vulnerability to gap-targeted DNA repair inhibitors.