The ability of human induced pluripotent stem cells (hiPSCs) to differentiate in vitro to each of the three germ layer lineages has made them an important model of early human development and a tool for tissue engineering. However, the factors that disturb the intricate transcriptional choreography of differentiation remain incompletely understood. Here, we uncover a critical time window during which DNA damage significantly reduces the efficiency and fidelity with which hiPSCs differentiate to definitive endoderm. DNA damage prevents the normal reduction of p53 levels as cells pass through the epithelial-to-mesenchymal transition, diverting the transcriptional program toward mesoderm without induction of an apoptotic response. In contrast, TP53-deficient cells differentiate to endoderm with high efficiency after DNA damage, suggesting that p53 enforces a "differentiation checkpoint" in early endoderm differentiation that alters cell fate in response to DNA damage.