Hydroxyapatite (HAp) is a bioactive ceramic with great potential for the regeneration of the skeletal system. However, its mechanical properties, especially its brittleness, limit its application. Therefore, in order to increase its ability to transmit stresses, it can be combined with a polymer phase, which increases its strength without eliminating the important aspect of bioactivity. The presented work focuses on obtaining organic–inorganic hydrogel materials based on whey protein isolate (WPI) reinforced with nano-HAp powder. The proportion of the ceramic phase was in the range of 0–15%. Firstly, a physicochemical analysis of the materials was performed using XRD, FT-IR and SEM. The hydrogel composites were subjected to swelling capacity measurements, potentiometric and conductivity analysis, and in vitro tests in four liquids: distilled water, Ringer’s fluid, artificial saliva, and simulated body fluid (SBF). The incubation results demonstrated the successful formation of new layers of apatite as a result of the interaction with the fluids. Additionally, the influence of the materials on the metabolic activity according to ISO 10993-5:2009 was evaluated by identifying direct contact cytotoxicity towards L-929 mouse fibroblasts, which served as a reference. Moreover, the stimulation of monocytes by hydrogels via the induction of nuclear factor (NF)-κB was investigated. The WPI/HAp composite hydrogels presented in this study therefore show great potential for use as novel bone substitutes.