Biomimetic, strain‐stiffening materials are reported, made through self‐assembly and covalent fixation of small building blocks to form fibrous hydrogels that are able to stiffen by an order of magnitude in response to applied stress. The gels consist of semi‐flexible rodlike micelles of bisurea bolaamphiphiles with oligo(ethylene oxide) (EO) outer blocks and a polydiacetylene (PDA) backbone. The micelles are fibers, composed of 9–10 ribbons. A gelation method based on Cu‐catalyzed azide–alkyne cycloaddition (CuAAC), was developed and shown to lead to strain‐stiffening hydrogels with unusual, yet universal, linear and nonlinear stress–strain response. Upon gelation, the X‐ray scattering profile is unchanged, suggesting that crosslinks are formed at random positions along the fiber contour without fiber bundling. The work expands current knowledge about the design principles and chemistries needed to achieve fully synthetic, biomimetic soft matter with on‐demand, targeted mechanical properties.