Although mutations leading to a compromised nuclear envelope cause diseases such as muscular dystrophies or accelerated aging, the consequences of mechanically induced nuclear envelope ruptures are less known. Here, we show that nuclear envelope ruptures induce DNA damage that promotes senescence in non-transformed cells and induces an invasive phenotype in human breast cancer cells. We find that the endoplasmic reticulum (ER)-associated exonuclease TREX1 translocates into the nucleus after nuclear envelope rupture and is required to induce DNA damage. Inside the mammary duct, cellular crowding leads to nuclear envelope ruptures that generate TREX1-dependent DNA damage, thereby driving the progression of in situ carcinoma to the invasive stage. DNA damage and nuclear envelope rupture markers were also enriched at the invasive edge of human tumors. We propose that DNA damage in mechanically challenged nuclei could affect the pathophysiology of crowded tissues by modulating proliferation and extracellular matrix degradation of normal and transformed cells.