The natural biomolecules of peptides and proteins are able to form elegant metal incorporating supramolecular nanomaterials through multiple weak non-covalent interactions. The use of toxic chemical reagents to fabricate silver nanoparticles poses a danger to apply them in various biomedical applications. Peptide and protein biomolecules have the potential to overcome this barrier by the supramolecular chemistry approach. In this review, we focus on the self-assembly of peptides and proteins to synthesize silver incorporating supramolecular nanoarchitectures, which in turn enhance the biological properties of these silver nanomaterials being used in nanomedicine. This review aims to illustrate the recent developments in amphiphilic peptides, oligopeptides, collagen, bovine serum albumin (BSA), and human serum albumin (HSA) as capping, stabilizing, and reducing agents to form silver incorporating supramolecular nanostructures. Finally, we provide some biomedical applications of silver-incorporating supramolecular nanomaterials along with future perspectives.