Copper and zinc nanoparticles have been suggested as potent anticancer agents, particularly against osteosarcoma, a highly aggressive bone cancer with limited treatment options. In order to avoid systemic toxicity, biomolecular carriers able to chelate metal ions and deliver them in a targeted manner to the vicinity of cancer cells need to be developed. Herein, we have used a histidine-containing, cyclic dipeptide as a carrier able to chelate stabilized copper and zinc nanoparticles. The cyclic peptide cyclo-(histidine-phenylalanine) (cHF) self-assembled into amyloid-type fibrils; morphological and structural characterization following metal addition confirmed the formation of cHF−CuNPs and cHF–ZnNPs. These composite nanoparticles demonstrated bacteriostatic activity against Escherichia coli and Staphylococcus aureus at the in vitro level. We evaluated the optimal concentration of cHF–metalNP complexes with limited cytotoxicity to L929 fibroblasts and high cytotoxic effects against MG-63 osteosarcoma cells. Their cytotoxicity was particularly pronounced at pH 6.4, which emulates the tumor microenvironment. The cHF peptide alone did not demonstrate significant antimicrobial or cytotoxic effects to both cell types, suggesting that it can act as a cytocompatible, pH-responsive carrier of metal ions with targeted dual functionality against both microbial infections and osteosarcoma cancer cells.