Migration through 3D constrictions can cause nuclear rupture and mislocalization of nuclear proteins, but damage to DNA remains uncertain, as does any effect on cell cycle. Here, myosin II inhibition rescues rupture and partially rescues the DNA damage marker γH2AX, but an apparent block in cell cycle appears unaffected. Co-overexpression of multiple DNA repair factors or antioxidant inhibition of break formation also exert partial effects, independently of rupture. Combined treatments completely rescue cell cycle suppression by DNA damage, revealing a sigmoidal dependence of cell cycle on excess DNA damage. Migration through custom-etched pores yields the same damage threshold, with ∼4-µm pores causing intermediate levels of both damage and cell cycle suppression. High curvature imposed rapidly by pores or probes or else by small micronuclei consistently associates nuclear rupture with dilution of stiff lamin-B filaments, loss of repair factors, and entry from cytoplasm of chromatin-binding cGAS (cyclic GMP-AMP synthase). The cell cycle block caused by constricted migration is nonetheless reversible, with a potential for DNA misrepair and genome variation.