The controllable delivery of drugs is a key task of pharmacology. For this purpose, a series of polymer composites was synthesized via the cross-linking of hyaluronate and a hyaluronate/polyacrylate mixture with Fe2O3 nanoparticles. The cross-linking imparts magnetic properties to the composites, which are more pronounced for the ternary hyaluronate/polyacrylate/γ-Fe2O3 composites compared with the binary hyaluronate/Fe2O3 composites. When dispersed in water, the composites produce microsized hydrogel particles. Circulation of the ternary microgels in an aqueous solution at a speed of 1.84 cm/s can be stopped using a permanent external magnet with a magnetic flux density of 400 T. The composite hydrogels can absorb the antitumor antibiotic doxorubicin (Dox); the resulting constructs show their cytotoxicity to tumor cells to be comparable to the cytotoxicity of Dox itself. The addition of the hyaluronidase enzyme induces degradation of the binary and ternary microgels down to smaller particles. This study presents prospectives for the preparation of magnetically controlled biodegradable polymer carriers for the encapsulation of bioactive substances.