Material extrusion is a widely employed additive manufacturing technique with the functional capability of fabricating solid objects or cellular structures by depositing molten thermoplastic material in successive layers according to the designed path of deposition beads. Carbon fiber sandwich composites are advanced structures, ideal in applications that require high strength and stiffness, and low weight. In the present work, sandwich composites consisting of a carbon fiber-reinforced polyamide core—3D printed with a cubic pattern at 50% infill density—and carbon fiber fabric skin, were fabricated using the hand lay-up method and experimentally investigated. The results showed that the tensile, flexural and impact strength of the sandwich composites increased by 64.5%, 24.5% and 69.0% respectively, compared to unreinforced 3D printed specimens with 50% infill density, and by 24.3%, 18.8% and 56.3% respectively, compared to unreinforced 3D printed specimens with 100% infill density. In addition, a reduction in the water absorption and the density of the sandwich composites was observed. Similar results were obtained for sandwich composites with one additional internal CFF layer. This work demonstrates that this specific combination of materials and manufacturing processes can be successfully employed for lightweight, water-resistant carbon fiber sandwich structures with improved mechanical strength.