Biosynthesis of nanomaterials is gaining attention as a sustainable, environmentally friendly, and reliable method for manufacturing a extensive array of nanostructures, such as metal/metal oxides and organic and hybrid materials. Green synthesis is considered a crucial tool to reduce the harsh effects associated with conventional synthesis. Nanocomposite materials containing biosynthesized nanostructures are highly sought after in regenerative medicine. In the present Review, biosynthesis of metal/metal oxides and carbon-based nanomaterials using microorganisms (e.g., bacteria and fungi) and natural compounds (e.g., polysaccharides, proteins, fruit juices, and plant extracts) is highlighted. The toxicity of biosynthesized nanoparticles for biomedical application is also reviewed in depth. The applications of bionanocomposites prepared from these ecofriendly nanoparticles in tissue engineering are reviewed to provide readers with a background for future studies.