Defects in ribosome biogenesis and function are present in a growing list of human syndromes associated with cancer susceptibility. One example is X‐linked dyskeratosis congenita (X‐DC) in which the DKC1 gene, encoding for an enzyme that modifies ribosomal RNA, is found to be mutated. How ribosome dysfunction leads to cancer remains poorly understood. A critical cellular response that counteracts cellular transformation is oncogene‐induced senescence (OIS). Here, we show that during OIS, a switch between cap‐ and internal ribosome entry site (IRES)‐dependent translation occurs. During this switch, an IRES element positioned in the 5′untranslated region of p53 is engaged and facilitates p53 translation. We further show that in DKC1^m cells, p53 IRES‐dependent translation is impaired during OIS ex vivo and on DNA damage in vivo. This defect in p53 translation perturbs the cellular response that counteracts oncogenic insult. We extend these findings to X‐DC human patient cells in which similar impairments in p53 IRES‐dependent translation are observed. Importantly, re‐introduction of wild‐type DKC1 restores p53 expression in these cells. These results provide insight into the basis for cancer susceptibility in human syndromes associated with ribosome dysfunction.