[Ni0.4Cu0.2Zn0.4](Fe2–xDyx)O4 spinel ferrite nanoparticles with different Dy3+ concentrations (0.00 ≤ x ≤ 0.04) were prepared by a citrate sol–gel auto-combustion technique. A strong correlation among Dy concentration, structural parameters, and magnetic, electrical, and microwave properties was established. An increase in the Dy3+ concentration is the reason for a rise in the crystal structure parameters (due to different ionic radii of Fe and Dy ions) and a slight increase in the average particle size with a minor reduction in the specific surface area. It was observed that Dy3+ ions prefer to occupy the octahedral B site due to their large ionic radius (0.91 Å). The explanation of the electrical and magnetic properties was given in terms of the features of Dy3+–O2––Fe3+ dysprosium–oxygen–iron indirect exchange. The occurrence of the intensive changes in amplitude–frequency characteristics was observed from 1.6 to 2.7 GHz. The explanation of electromagnetic absorption was given in terms of the peculiarities of the microstructure (resonance of domain boundaries). The results open perspectives in the utilization of [Ni0.4Cu0.2Zn0.4](Fe2–xDyx)O4 spinel ferrite nanoparticles as functional materials for targeted drug delivery and hyperthermia applications.