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Biomaterials with outstanding mechanical properties, including spider silk, wood, and cartilage, often feature an oriented nanofibrillar structure. The orientation of nanofibrils gives rise to a significant mechanical anisotropy, which is extremely challenging to characterize, especially for microscopically small or inhomogeneous samples. Here, a technique utilizing atomic force microscope indentation at multiple points combined with finite element analysis to sample the mechanical anisotropy of a thin film in a microscopically small area is reported. The system studied here is the tape‐like silk of the Chilean recluse spider, which entirely consists of strictly oriented nanofibrils giving rise to a large mechanical anisotropy. The most detailed directional nanoscale structure–property characterization of spider silk to date is presented, revealing the tensile and transverse elastic moduli as 9 and 1 GPa, respectively, and the binding strength between silk nanofibrils as 159±13 MPa. Furthermore, based on this binding strength, the nanofibrils’ surface energy is derived as 37 mJ m⁻², and concludes that van der Waals forces play a decisive role in interfibrillar binding. Due to its versatility, this technique has many potential applications, including early disease diagnostics, as underlying pathological conditions can alter the local mechanical properties of tissues.