The formation of a new head during Hydra regeneration involves the establishment of a head organizer that functions as a signaling center and contains an aster-shaped topological defect in the organization of the supracellular actomyosin fibers. Here, we show that the future head region in regenerating tissue fragments undergoes multiple instances of extensive stretching and rupture events from the onset of regeneration. These recurring localized tissue deformations arise due to transient contractions of the supracellular ectodermal actomyosin fibers that focus mechanical strain at defect sites. We further show that stabilization of aster-shaped defects is disrupted by perturbations of the Wnt signaling pathway. We propose a closed-loop feedback mechanism promoting head organizer formation, and develop a biophysical model of regenerating Hydra tissues that incorporates a morphogen source activated by mechanical strain and an alignment interaction directing fibers along morphogen gradients. We suggest that this positive-feedback loop leads to mechanical strain focusing at defect sites, enhancing local morphogen production and promoting robust organizer formation.