Sodium alginate and tannic acid are natural compounds that can be mixed with each other. In this study, we propose novel eco-friendly hydrogels for biomedical applications. Thus, we conducted the following assessments including (i) observation of the structure of hydrogels by scanning electron microscope; (ii) bioerosion and the concentration of released tannic acid from subjected material; (iii) dehydrogenase activity assay to determine antibacterial activity of prepared hydrogels; and (iv) blood and cell compatibility. The results showed that hydrogels based on sodium alginate/tannic acid exert a porous structure. The immersion in simulated body fluid (SBF) results in the biomineralization process occurring on their surface while the bioerosion studies revealed that the addition of tannic acid improves hydrogels’ stability proportional to its concentration. Besides, tannic acid release concentration depends on the type of hydrogels and the highest amount was noticed for those based on sodium alginate with the content of 30% tannic acid. Antibacterial activity of hydrogels was proven for both Gram-negative and Gram-positive bacteria, the hemolysis rate was below 5% and the viability of the cells was elevated with an increasing amount of tannic acid in hydrogels. Collectively, we assume that obtained materials make the imperative to consider them for biomedical applications.