Fanconi anemia (FA) is an inherited DNA repair deficiency syndrome. FA patients undergo progressive bone marrow failure (BMF) during childhood, which frequently requires allogeneic hematopoietic stem cell transplantation. The pathogenesis of this BMF has been elusive to date. Here we found that FA patients exhibit a profound defect in hematopoietic stem and progenitor cells (HSPCs) that is present before the onset of clinical BMF. In response to replicative stress and unresolved DNA damage, p53 is hyperactivated in FA cells and triggers a late p21^Cdkn1a-dependent G0/G1 cell-cycle arrest. Knockdown of p53 rescued the HSPC defects observed in several in vitro and in vivo models, including human FA or FA-like cells. Taken together, our results identify an exacerbated p53/p21 "physiological" response to cellular stress and DNA damage accumulation as a central mechanism for progressive HSPC elimination in FA patients, and have implications for clinical care.