Many bacteria are motile by means of one or more rotating rigid helical flagella, making them the only known organism to use rotation as a means of propulsion. The rotation is supplied by the bacterial flagellar motor, a particularly powerful rotary molecular machine. At the base of each flagellum is the hook, a soft helical polymer that acts as a universal joint, coupling rotation of the rigid membrane-spanning rotor to rotation of the rigid extra-cellular flagellum. In multi-flagellated bacterial species, where thrust is provided by a hydrodynamically coordinated bundle of flagella, the flexibility of the hook is particularly crucial, as many of the flagella within the bundle rotate significantly off-axis from their motor. But, consequently, the thrust produced by a single rotating flagellum applies a significant bending moment to the hook. So, the hook needs to simultaneously provide the compliance necessary for off-axis bundle formation and the rigidity necessary to withstand the large hydrodynamical forces of swimming. To elucidate how the hook can fulfill this double functionality, measurements of the mechanical behavior of individual hooks under dynamical conditions are needed. Here, via new high-resolution measurements and a novel analysis of hook fluctuations during in vivo motor rotation in bead assays, we resolve the elastic response of single hooks under increasing torsional stress, revealing a clear dynamic increase in their bending stiffness. Accordingly, the persistence length of the hook increases by more than one order of magnitude with applied torque. Such strain-stiffening allows the system to be flexible when needed yet reduce deformation under high loads, allowing cellular motility at high speed.