Mineralization processes based on co-precipitation methods have been applied as a promising alternative to the most commonly used methods of polymer–ceramic combination, direct mixing, and incubation in simulated body fluid (SBF) or modified SBF. In the present study, for the first time, the in situ mineralization (ideally hydroxyapatite formation) of blue shark (Prionace glauca (PG)) collagen to fabricate 3D printable cell-laden hydrogels is proposed. In the first part, several parameters for collagen mineralization were tested until optimization. The hydroxyapatite formation was confirmed by FTIR, XRD, and TEM techniques. In the second part, stable bioinks combining the biomimetically mineralized collagen with alginate (AG) (1:1, 1:2, 1:3, and AG) solution were used for 3D printing of hydrogels. The addition of Ca2+ ions into the system did present a synergistic effect: by one side, the in situ mineralization of the collagen occurred, and at same time, they were also useful to ionically crosslink the blends with alginate, avoiding the addition of any cytotoxic chemical crosslinking agent. Mouse fibroblast cell line survival during and after printing was favored by the presence of PG collagen as exhibited by the biological performance of the hydrogels. Inspired in a concept of marine byproduct valorization, 3D bioprinting of in situ mineralized blue shark collagen is thus proposed as a promising approach, envisioning the engineering of mineralized tissues.