Currently, the main drawback of ceramic scaffolds used in hard tissue regeneration is their low mechanical strength. Stabilized zirconia, especially the tetragonal 3% yttrium-stabilized zirconia (YSZ) phase, has been considered as a bioinert ceramic material with high mechanical strength. In the present work, flexible nanofibrous YSZ scaffolds were prepared by electrospinning. The obtained scaffolds showed remarkable flexibility at the macroscopic scale, while retaining their stiffness at the microscopic scale. The surface nanoroughness of the scaffolds could be tailored by varying the heat treatment method. Our results demonstrate that the osteogenic differentiation and mineralization of seeded human mesenchymal stromal cells were supported by the nanofibrous YSZ scaffolds, in contrast to the well-known bioinert behavior of bulk YSZ. These findings highlight that flexible ceramic scaffolds are an appealing alternative to the current brittle ceramics for bone tissue regeneration applications.