Tissue engineered constructs prepared using conventional scaffold-based approaches have the potential to repair or regenerate damaged tissues and organs. Various scaffold fabrication strategies such as electrospinning, solvent casting, particulate leaching, gas foaming, hydrogels, freeze-drying, and 3D bioprinting have been used to fabricate artificial tissues. In recent times, 3D bioprinting has been predominantly used in various biomedical fields, including healthcare and pharmaceutical applications due to precision in 3D geometry. However, there are no viable strategies to preserve bioprinted constructs for on-demand applications because of the lack of specialized techniques or cryopreservation agents to maintain the cell viability and functionality of the bioprinted tissues. To solve this issue, cryopreservation of bioprinted tissues has emerged in recent years to develop methods to create and cryopreserve bioprinted constructs for on-demand applications. This review discusses various techniques used for producing ready-to-use tissue engineered products such as electrospinning, hydrogels, 3D bioprinting, and other bioprinting approaches. Further, the factors influencing the bioprinted tissues, such as cryoprotectants, polymer types and crosslinker concentrations, crosslinking approaches, viscoelastic properties, storage facilities, etc, were also discussed in detail. The potential of cryopreservable bioprinted tissues in various healthcare applications are elaborated with lucid examples. Finally, the conclusions and possible future directions for the fabrication and cryopreservation of tissue engineered products are highlighted.