Polymers of natural origin, such as representatives of various polysaccharides (e.g., cellulose, dextran, hyaluronic acid, gellan gum, etc.), and their derivatives, have a long tradition in biomedical applications. Among them, the use of chitosan as a safe, biocompatible, and environmentally friendly heteropolysaccharide has been particularly intensively researched over the last two decades. The potential of using chitosan for medical purposes is reflected in its unique cationic nature, viscosity-increasing and gel-forming ability, non-toxicity in living cells, antimicrobial activity, mucoadhesiveness, biodegradability, as well as the possibility of chemical modification. The intuitive use of clay minerals in the treatment of superficial wounds has been known in traditional medicine for thousands of years. To improve efficacy and overcome the ubiquitous bacterial resistance, the beneficial properties of chitosan have been utilized for the preparation of chitosan-clay mineral bionanocomposites. The focus of this review is on composites containing chitosan with montmorillonite and halloysite as representatives of clay minerals. This review highlights the antibacterial efficacy of chitosan-clay mineral bionanocomposites in drug delivery and in the treatment of topical skin infections and wound healing. Finally, an overview of the preparation, characterization, and possible future perspectives related to the use of these advancing composites for biomedical applications is presented.