Hydrogels based on gelatin–chitosan mixtures have great potential for practical application in the development of new materials in food technology and biomedicine. This study examines the effect of chitosan on the gelling properties, rheological, and structural characteristics of fish gelatin type A hydrogels in the acidic pH range of 3.2–3.9. It was shown that an increase in the chitosan-to-gelatin mass ratio up to 0.15 resulted in a growth in the hydrogel thermal stability and an increase in the elastic modulus, hardness, and yield stress. The structural strength of the fish gelatin–chitosan hydrogel increased due to the strengthening of the binding zones in the fish gelatin gel network in the presence of chitosan. According to scanning electron microscopy, the supramolecular microstructure of the gels demonstrated a significant compaction upon the addition of chitosan to fish gelatin. UV and IR spectroscopy data, as well as changes in zeta potential, showed the formation of supramolecular complexes of fish gelatin with chitosan as a result of hydrophobic interactions between biomacromolecules and the establishment of hydrogen bonds; in this case, electrostatic interactions between macromolecules of fish gelatin and chitosan are practically absent in the acidic pH region. The ability to form supramolecular complexes of different compositions at different mass ratios of polysaccharide-to-fish gelatin makes it possible to obtain hydrogels with high gelling properties, strength, elasticity, and thermal stability comparable to hydrogels of mammalian gelatin.