T₂^⁎-weighted MRI at high field is a promising approach for studying noninvasively the tissue structure and composition of the brain. However, the biophysical origin of T₂^⁎ contrast, especially in white matter, remains poorly understood. Recent work has shown that R₂^⁎ (=1/T₂^⁎) may depend on the tissue's orientation relative to the static magnetic field (B₀) and suggested that this dependence could be attributed to local anisotropy in the magnetic properties of brain tissue. In the present work, we analyzed high-resolution, multi-gradient-echo images of in vivo marmoset brains at 7T, and compared them with ex vivo diffusion tensor images, to show that R₂^⁎ relaxation in white matter is highly sensitive to the fiber orientation relative to the main field. We directly demonstrate this orientation dependence by performing in vivo multi-gradient-echo experiments in two orthogonal brain positions, uncovering a nearly 50% change in the R₂^⁎ relaxation rate constant of the optic radiations. We attribute this substantial R₂^⁎ anisotropy to local subvoxel susceptibility effects arising from the highly ordered and anisotropic structure of the myelin sheath.