Inactivating p53 mutations are the most abundant genetic alterations found in cancer. Here we show that CRISPR/Cas9-induced double-stranded DNA breaks enrich for cells deficient in p53 as well as in genes of a core CRISPR-p53 tumor suppressor interactome. Such enrichment could predispose to cancer development and thus pose a challenge for clinical CRISPR use. Transient p53 inhibition could suppress the enrichment of cells with these mutations. The level of DNA damage response induced by an sgRNA influenced the enrichment of p53 deficient cells and could be a relevant parameter in sgRNA design to limit cellular enrichment. Furthermore, a dataset of >800 human cancer cell lines identified additional factors influencing the enrichment of p53 mutated cells, including strong baseline CDKN1A expression as a predictor for an active CRISPR-p53 axis. Taken together, these data provide details about p53 biology in the context of CRISPR-induced DNA damage and identify strategies to enable safer CRISPR use.