Amorphous solids are randomly disordered without any long-range periodic atomic arrangement and thus appear isotropic. Here, we show in metallic glasses that this view does not hold at small scales: Strong mechanical anisotropy emerges when the sample size decreases below about 15 nm as shown by the marked deviation in stress-strain relations as well as elastic modulus along different loading directions. The size induced mechanical anisotropy is naturally related to structural anisotropy that is absent before loading. The anisotropic stress and modulus versus the size yield different scaling exponents in different stages of deformation, hinting at different deformation mechanisms. The size effect discovered here points to the existence of intrinsic heterogeneity defined by the anisotropy, which may play an important role in structure-property relations in amorphous solids.