Morphogenesis is a process in which a well-defined pattern of functional tissues emerges during the development of an organism. One of the great challenges in morphogenesis research is understanding the organizational principles responsible for the robust convergence of the process, across scales, to form viable organisms under variable conditions. In our research we utilize the fresh water animal Hydra as a model system to study the role of mechanics in morphogenesis, focusing on the dynamics of the actin cytoskeleton during a regeneration process which is akin to development. Here we show that the nematic order of the supra-cellular actin fibres in regenerating Hydra defines a slowly-varying field, whose dynamics provide an effective description of the morphogenesis process. The nematic orientation field necessarily contains defects constrained by the topology of the regenerating tissue. These nematic topological defects are long-lived, yet display rich dynamics that can be related to the major morphological events during regeneration. In particular, we show that these defects act as organizing centres, with the main functional morphological features developing at defect sites. These results suggest a system of self-organization involving the actin cytoskeleton in the regenerating tissue that is based on mechanical feedback, and provide, to our knowledge, the first demonstration of the significance of topological defects in nematic organization for establishing the body plan of a living animal.