Composites based on acrylonitrile–butadiene rubber, carbon nanotubes, and manganese–zinc ferrite were fabricated and tested for electromagnetic interference (EMI) absorption shielding. First, carbon nanotubes and ferrite were solely used for the preparation of rubber composites. Then, carbon nanotubes were combined with magnetic filler and incorporated into the rubber matrix. The results revealed that carbon nanotubes act as reinforcing filler and significantly enhance the physical–mechanical properties of composites. The presence of carbon nanotubes in the rubber matrix also results in an outstanding increase in electrical conductivity and permittivity of composite materials, as a consequence of which the EMI absorption shielding was poor in the tested frequency range of 1 MHz to 3 GHz. On the other hand, ferrite-filled composites are able to efficiently absorb electromagnetic radiation emitted from various electronic and radiation sources. However, the tensile strength of the composites showed a decreasing trend with increasing content of ferrite. The combination of carbon nanotubes with manganese–zinc ferrite resulted in an improvement in the physical–mechanical properties of hybrid composites. As the permittivity of hybrid composites was still much higher in comparison with those filled only with ferrite, only the composite filled with 5 phr of carbon nanotubes and 100 phr of ferrite showed a slight EMI absorption shielding ability over the tested frequency range.