The aim of this work was to study the effect of cryopreservation over the functionality of tissue-engineered constructs, analyzing the survival and viability of cells seeded, cultured, and cryopreserved onto 3D scaffolds. Further, it also evaluated the effect of cryopreservation over the properties of the scaffold material itself since these are critical for the engineering of most tissues and in particular, tissues such as bone. For this purpose, porous scaffolds, namely fiber meshes based on a starch and poly(caprolactone) blend were seeded with goat bone marrow stem cells (GBMSCs) and cryopreserved for 7 days. Discs of the same material seeded with GBMSCs were also used as controls. After this period, these samples were analyzed and compared to samples collected before the cryopreservation process. The obtained results demonstrate that it is possible to maintain cell viability and scaffolds properties upon cryopreservation of tissue-engineered constructs based on starch scaffolds and goat bone marrow mesenchymal cells using standard cryopreservation methods. In addition, the outcomes of this study suggest that the greater porosity and interconnectivity of scaffolds favor the retention of cellular content and cellular viability during cryopreservation processes, when compared with nonporous discs. These findings indicate that it might be possible to prepare off-the-shelf engineered tissue substitutes and preserve them to be immediately available upon request for patients' needs.