The mutagenic APOBEC3B (A3B) cytosine deaminase is frequently over-expressed in cancer and promotes tumour heterogeneity and therapy resistance. Hence, understanding the mechanisms that underlie A3B over-expression is important, especially for developing therapeutic approaches to reducing A3B levels, and consequently limiting cancer mutagenesis. We previously demonstrated that A3B is repressed by p53 and p53 mutation increases A3B expression. Here, we investigate A3B expression upon treatment with chemotherapeutic drugs that activate p53, including 5-fluorouracil, etoposide and cisplatin. Contrary to expectation, these drugs induced A3B expression and concomitant cellular cytosine deaminase activity. A3B induction was p53-independent, as chemotherapy drugs stimulated A3B expression in p53 mutant cells. These drugs commonly activate ATM, ATR and DNA-PKcs. Using specific inhibitors and gene knockdowns, we show that activation of DNA-PKcs and ATM by chemotherapeutic drugs promotes NF-κB activity, with consequent recruitment of NF-κB to the A3B gene promoter to drive A3B expression. Further, we find that A3B knockdown re-sensitises resistant cells to cisplatin, and A3B knockout enhances sensitivity to chemotherapy drugs. Our data highlight a role for A3B in resistance to chemotherapy and indicate that stimulation of A3B expression by activation of DNA repair and NF-κB pathways could promote cancer mutations and expedite chemoresistance.