The synthesis of methanol and dimethyl ether (DME) from carbon dioxide (CO2) and green hydrogen (H2) offers a sustainable pathway to convert CO2 emissions into value-added products. This heterogeneous catalytic reaction often uses copper (Cu) catalysts due to their low cost compared with their noble metal analogs. Nevertheless, improving the activity and selectivity of these Cu catalysts for these products is highly desirable. In the present study, a new architecture of Cu- and Cu/Zn-based catalysts supported on electrospun alumina nanofibers were synthesized. The catalysts were tested under various reaction conditions using high-throughput equipment to highlight the role of the hierarchical fibrous structure on the reaction activity and selectivity. The Cu or Cu/ZnO formed a unique structure of nanosheets, covering the alumina fiber surface. This exceptional morphology provides a large surface area, up to ~300 m2/g, accessible for reaction. Maximal production of methanol (~1106 gmethanolKgCu−1∙h−1) and DME (760 gDMEKgCu−1∙h−1) were obtained for catalysts containing 7% wt. Cu/Zn with a weight ratio of 2.3 Zn to Cu (at 300 °C, 50 bar). The promising results in CO2 hydrogenation to methanol and DME obtained here point out the significant advantage of nanofiber-based catalysts in heterogeneous catalysis.