Composite materials are popular substitutes for conventional materials owing to their high strength-to-weight ratio. Reinforcements in the form of woven fabric clothes are common due to their ease of availability and preparation. The use of hybrid intra-ply as reinforcements synergises the advantages of more than one type of fibre. The current work focuses on the preparation of woven carbon fibre (CF) and carbon–Kevlar (CF-K) intra-ply hybrid fibre-based composites. Epoxy resin was used as the matrix and balsa sheet was used as the sandwich material. The angle of orientation of the woven fibre cloth was varied from 0° to 45° along the direction of loading. The dynamic properties of prepared samples were experimentally investigated using an impact hammer test. The natural frequency and damping ratio were influenced by the angle of orientation and the fibre reinforcement. The CF-K hybrid composite showed better dynamic properties when compared with the CF composite. The natural frequency was highest for the 0° sample, it reduced with the angle of orientation, and a reverse trend was observed for damping ratio. Both CF- and CF-K-based composites showed similar trends. The storage modulus variation also showed a similar trend as that of the natural frequency for both types of samples with orientation, but a reverse trend was observed for loss modulus, i.e., the loss modulus increased with the change in the angle of orientation, indicating the improvement in energy storage ability of the composite.