Biodegradable and biocompatible polymers are actively used in tissue engineering to manufacture scaffolds. Biomedical properties of polymer scaffolds depend on the physical and chemical characteristics and biodegradation kinetics of the polymer material, 3D microstructure and topography of the scaffold surface, as well as availability of minerals, medicinal agents, and growth factors loaded into the scaffold. However, in addition to the above, the intrinsic biological activity of the polymer and its biodegradation products can also become evident. This review provides studies demonstrating that scaffolds made of poly(3-hydroxybutyrate) (PHB) and its copolymers have their own biological activity, and namely, osteoinductive properties. PHB can induce differentiation of mesenchymal stem cells in the osteogenic direction in vitro and stimulates bone tissue regeneration during the simulation of critical and non-critical bone defects in vivo.