Errors during cell division lead to aneuploidy, which is associated with genomic instability and cell transformation. In response to aneuploidy, cells activate the tumour suppressor p53 to elicit a surveillance mechanism that halts proliferation and promotes senescence. The molecular sensors that trigger this checkpoint are unclear. Here, using a tunable system of chromosome mis-segregation, we show that mitotic errors trigger nuclear deformation, nuclear softening, and lamin and heterochromatin alterations, leading to rapid p53/p21 activation upon mitotic exit in response to changes in nuclear mechanics. We identify mTORC2 and ATR as nuclear deformation sensors upstream of p53/p21 activation. While triggering mitotic arrest, the chromosome mis-segregation-induced alterations of nuclear envelope mechanics provide a fitness advantage for aneuploid cells by promoting nuclear deformation resilience and enhancing pro-invasive capabilities. Collectively, this work identifies a nuclear mechanical checkpoint triggered by altered chromatin organization that probably plays a critical role in cellular transformation and cancer progression.