The structure, morphology and magnetic properties of ZnxCo0.8−xNi0.4Fe2O4 @SiO2 (x = 0.1; 0.3; 0.5; 0.7) nanocomposites (NCs) were investigated. The formation of the ferrites and SiO2 matrix was confirmed by X-ray diffraction that indicated the presence of low-crystalline single-phase Ni-Zn-Co spinel ferrite at 500 °C, well-crystallized Ni-Zn-Co spinel ferrite accompanied by Fe2SiO4 at 800 °C and by crystalline SiO2 (tridymite and cristobalite) at 1100 °C. In NCs with high Zn2+ content annealed at 1100 °C, traces of α-Fe2O3 were also noticed. The average crystallite size increased from 9.56 to 38.0 nm with the increase of annealing temperature and decreased with the increase of Zn2+ content. The scanning electron microscopy revealed large aggregates of irregular shapes. The transmission electron microscopy revealed the presence of both small and large spherical particles with a tendency to form agglomerates. The increase of Zn2+ content led to an increase of the number of low-size particles. The investigated NCs with high Co2+ content annealed at 1100 °C displayed ferrimagnetic behavior, while those with high Zn2+ content exhibited superparamagnetic behavior. The magnetic properties (saturation magnetization, remanent magnetization, coercivity and anisotropy) evolved proportionally with the particle size and Co2+ content for the NCs annealed at 800 and 1100 °C, which is of high significance for possible applications in biomedicine as carriers for targeted drug delivery, hyperthermia treatment or magnetic resonance imaging agents.