Hydrogel materials based on sodium alginate find versatile applications in regenerative medicine and tissue engineering due to their unique properties, such as biocompatibility and biodegradability, and the possibility of the customization of their mechanical properties, such as in terms of the individual requirements of separate clinical applications. These materials, however, have numerous limitations in the area of biological activity. In order to eliminate their limitations, sodium alginate is popularly applied in combination with added gelatin, which represents a product of collagen hydrolysis. Despite numerous beneficial biological properties, matrix materials based on gelatin have poor mechanical properties and are characterized by their ability for rapid degradation in an aqueous environment, particularly at the physiological temperature of the body, which significantly limits the independent application opportunities of this type of composition in the range of scaffolding production dedicated for tissue engineering. Collagen hydrogels, unlike gelatin, are characterized by higher bioactivity, dictated by a greater number of ligands that allow for cell adhesion, as well as better stability under physiological conditions. Fish-derived collagen provides a material that may be efficiently extracted without the risk of mammalian prion infection and can be used in all patients without religious restrictions. Considering the numerous advantages of collagen indicating its superiority over gelatin, within the framework of this study, the compositions of hydrogel materials based on sodium alginate and fish collagen in different concentrations were developed. Prepared hydrogel materials were compared with the properties of a typical composition of alginate with the addition of gelatin. The rheological, mechanical, and physicochemical properties of the developed polymer compositions were evaluated. The first trials of 3D printing by extrusion technique using the analyzed polymer solutions were also conducted. The results obtained indicate that replacing gelatin with fish collagen at an analogous concentration leads to obtaining materials with a lower swelling degree, better mechanical properties, higher stability, limited release kinetics of calcium ions cross-linking the alginate matrix, a slowed process of protein release under physiological conditions, and the possibility of extrusion 3D printing. The conducted analysis highlights that the optimization of the applied concentrations of fish collagen additives to composition based on sodium alginate creates the possibility of designing materials with appropriate mechanical and rheological properties and degradation kinetics adjusted to the requirements of specific applications, leading to the prospective opportunity to produce materials capable of mimicking the properties of relevant soft tissues. Thanks to its excellent bioactivity and lower-than-gelatin viscosity of the polymer solution, fish collagen also provides a prospective solution for applications in the field of 3D bioprinting.