Tissue regeneration at an injured site depends on proliferation, migration, and differentiation of resident stem or progenitor cells, but solid tissues are often sufficiently dense and constricting that nuclei are highly stressed by migration. In this study, constricted migration of myoblastic cell types and mesenchymal stem cells (MSCs) increases nuclear rupture, increases DNA damage, and modulates differentiation. Fewer myoblasts fuse into regenerating muscle in vivo after constricted migration in vitro, and myodifferentiation in vitro is likewise suppressed. Myosin II inhibition rescues rupture and DNA damage, implicating nuclear forces, while mitosis and the cell cycle are suppressed by constricted migration, consistent with a checkpoint. Although perturbed proliferation fails to explain defective differentiation, nuclear rupture mislocalizes differentiation-relevant MyoD and KU80 (a DNA repair factor), with nuclear entry of the DNA-binding factor cGAS. Human MSCs exhibit similar damage, but osteogenesis increases-which is relevant to bone and to calcified fibrotic tissues, including diseased muscle. Tissue repair can thus be modulated up or down by the curvature of pores through which stem cells squeeze.