Cryopreservation of ready-made cell-biomaterial composites is an essential aspect of modern regenerative medicine and tissue engineering. However, in the freeze–thawing of adherent cells, a problem encountered is the detachment of cells due to the intracellular tensile stress caused by dehydration. To reduce the cell detachment, a scaffold that retains elasticity at freezing temperatures was investigated here for use in direct cryopreservation of adherent cells. We focused on electrospun polyurethane (PU) nanofiber sheets, which featured a lower glass-transition temperature than the freezing temperature used and presented a loose mesh-like structure of nanofibers. Consequently, the recovery of cells cultured on the PU nanofiber sheets and then freeze–thawed was higher than the recovery of cells cultured on polystyrene films and fibers. Furthermore, higher cell recovery was obtained with randomly oriented PU nanofibers than with highly aligned PU nanofibers. These results suggest that the elasticity of the polymer and the looseness of the fiber mesh are key factors that enhance the recovery of adherent cells after freeze–thawing. This is the first report demonstrating that the elastic nanofiber scaffold is an available material that enables the cryopreservation of adherent cells; the use of this scaffold could substantially improve the cryopreservation outcome of cell-biomaterial composites.