Spider dragline silk possesses superior mechanical properties(1,2) compared with synthetic polymers with similar chemical structure due to its hierarchical structure comprised of partially crystalline oriented nanofibrils(3,4). To date, silk's dynamic mechanical properties have been largely unexplored. Here we report an indirect hypersonic phononic bandgap and an anomalous dispersion of the acoustic-like branch from inelastic (Brillouin) light scattering experiments under varying applied elastic strains. We show the mechanical nonlinearity of the silk structure generates a unique region of negative group velocity, that together with the global (mechanical) anisotropy provides novel symmetry conditions for gap formation(5-8). The phononic bandgap and dispersion show strong non-linear strain-dependent behaviour. Exploiting material nonlinearity along with tailored structural anisotropy could be a new design paradigm to access new types of dynamic behaviour.