Triple‐negative breast cancer (TNBC) is an aggressive breast cancer subtype with limited treatment options and poor prognosis. There is an urgent need to identify and understand the key factors and signalling pathways driving TNBC tumour progression, relapse, and treatment resistance. In this study, we report that gene copy numbers and expression levels of nuclear factor IB (NFIB), a recently identified oncogene in small cell lung cancer, are preferentially increased in TNBC compared to other breast cancer subtypes. Furthermore, increased levels of NFIB are significantly associated with high tumour grade, poor prognosis, and reduced chemotherapy response. Concurrent TP53 mutations and NFIB overexpression (z‐scores > 0) were observed in 77.9% of TNBCs, in contrast to 28.5% in non‐TNBCs. Depletion of NFIB in TP53‐mutated TNBC cell lines promotes cell death, cell cycle arrest, and enhances sensitivity to docetaxel, a first‐line chemotherapeutic drug in breast cancer treatment. Importantly, these alterations in growth properties were accompanied by induction of CDKN1A, the gene encoding p21, a downstream effector of p53. We show that NFIB directly interacts with the CDKN1A promoter in TNBC cells. Furthermore, knockdown of combined p21 and NFIB reverses the docetaxel‐induced cell growth inhibition observed upon NFIB knockdown, indicating that NFIB's effect on chemotherapeutic drug response is mediated through p21. Our results indicate that NFIB is an important TNBC factor that drives tumour cell growth and drug resistance, leading to poor clinical outcomes. Thus, targeting NFIB in TP53‐mutated TNBC may reverse oncogenic properties associated with mutant p53 by restoring p21 activity. Copyright © 2018 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.