The most difficult issue when using tissue engineering products is enabling the ability to store them without losing their restorative capacity. The numbers and viability of mesenchymal stem cells encapsulated in a hydrogel scaffold after cryostorage at −80 °C (by using, individually, two kinds of cryoprotectors—Bambanker and 10% DMSO (Dimethyl sulfoxide) solution) for 3, 6, 9, and 12 months were determined, with subsequent assessment of cell proliferation after 96 h. The analysis of the cellular component was performed using fluorescence microscopy and the two fluorochromes—Hoechst 3334 and NucGreenTM Dead 488. The experimental protocol ensured the preservation of cells in the scaffold structure, retaining both high viability and proliferative activity during storage for 3 months. Longer storage of scaffolds led to their significant changes. Therefore, after 6 months, the proliferative activity of cells decreased. Cryostorage of scaffolds for 9 months led to a decrease in cells’ viability and proliferative activity. As a result of cryostorage of scaffolds for 12 months, a decrease in viability and proliferative activity of cells was observed, as well as pronounced changes in the structure of the hydrogel. The described scaffold cryostorage protocol could become the basis for the development of storage protocols for such tissue engineering products, and for helping to extend the possibilities of their clinical use while accelerating their commercialization.