Many problems related to disorders and defects of bone tissue caused by aging, diseases, and injuries have been solved by the multidisciplinary research field of regenerative medicine and tissue engineering. Numerous sciences, especially nanotechnology, along with tissue engineering, have greatly contributed to the repair and regeneration of tissues. Various studies have shown that the presence of magnetic nanoparticles (MNPs) in the structure of composite scaffolds increases their healing effect on bone defects. In addition, the induction of osteogenic differentiation of mesenchymal stem cells (MSCs) in the presence of these nanoparticles has been investigated and confirmed by various studies. Therefore, in the present article, the types of MNPs, their special properties, and their application in the healing of damaged bone tissue have been reviewed. Also, the molecular effects of MNPs on cell behavior, especially in osteogenesis, have been discussed. Finally, the present article includes the potential applications of MNP-containing nanocomposite scaffolds in bone lesions and injuries. In summary, this review article highlights nanocomposite scaffolds containing MNPs as a solution for treating bone defects in tissue engineering and regenerative medicine.