In recent years, there has been a significant increase in interest in the use of curdlan, a naturally derived polymer, for medical applications. However, it is relatively inactive, and additives increasing its biomedical potential are required; for example, antibacterial compounds, magnetic particles, or hemostatic agents. The stability of such complex constructs may be increased by additional functional networks, for instance, polycatecholamines. The article presents the production and characterization of functional hydrogels based on curdlan enriched with Fe3O4 nanoparticles (NPs) or Fe3O4–based heterostructures and poly(L-DOPA) (PLD). Some of the prepared modified hydrogels were nontoxic, relatively hemocompatible, and showed high antibacterial potential and the ability to convert energy with heat generation. Therefore, the proposed hydrogels may have potential applications in temperature-controlled regenerative processes as well as in oncology therapies as a matrix of increased functionality for multiple medical purposes. The presence of PLD in the curdlan hydrogel network reduced the release of the NPs but slightly increased the hydrogel’s hemolytic properties. This should be taken into account during the selection of the final hydrogel application.