In this work, the influence of the crystallographic orientation of high-purity aluminum single crystals of grade A999 on the transformation of the initial structure as a result of exposure to shock waves at a temperature of −196°C was experimentally investigated. It was found that when the shock front propagates in the [110] direction at pressures of 40 GPa and 50 GPa, structural changes in aluminum single crystals are observed in the form of dislocation slip lines along the (111) and (110) planes. The impact of the shock front in the direction of [113] at a pressure of 50 GPa leads to coordination structural changes. It was found that a nanocrystalline structure with an average grain size of 80 nm is formed in the near-surface layers at a depth of 1–3 mm, and a subgrain structure is formed at a depth of 6–7 mm. In fact, a gradient type structure is formed. The reasons for the pronounced effect of the influence of the crystallographic orientation of high-purity aluminum single crystals on structural changes under the action of shock waves are discussed.