The demand for regenerative medicine products is growing rapidly in clinical practice. Unfortunately, their use has certain limitations. One of these, which significantly constrains the widespread distribution and commercialization of such materials, is their short life span. For products containing suspensions of cells, this issue can be solved by using cryopreservation. However, this approach is rarely used for multicomponent tissue-engineered products due to the complexity of selecting appropriate cryopreservation protocols and the lack of established criteria for assessing the quality of such products once defrosted. Our research is aimed at developing a cryopreservation protocol for an original hydrogel scaffold with encapsulated MSCs and developing a set of criteria for assessing the quality of their functional activity in vitro. The scaffolds were frozen using two alternative types of cryocontainers and stored at either -40 °C or -80 °C. After cryopreservation, the external state of the scaffolds was evaluated in addition to recording the cell viability, visible changes during subsequent cultivation, and any alterations in proliferative and secretory activity. These observations were compared to those of scaffolds cultivated without cryopreservation. It was shown that cryopreservation at -80 °C in an appropriate type of cryocontainer was optimal for the hydrogels/adipose-derived stem cells (ASCs) tested if it provided a smooth temperature decrease during freezing over a period of at least three hours until the target values of the cryopreservation temperature regimen were reached. It was shown that evaluating a set of indicators, including the viability, the morphology, and the proliferative and secretory activity of the cells, enables the characterization of the quality of a tissue-engineered construct after its withdrawal from cryopreservation, as well as indicating the effectiveness of the cryopreservation protocol.