Copper (Cu) is a transition metal that plays crucial roles in cellular metabolism. Cu+ homeostasis is upregulated in many cancers and contributes to tumorigenesis. However, therapeutic strategies to target Cu+ homeostasis in cancer cells are rarely explored because small molecule Cu+ chelators have poor binding affinity in comparison to the intracellular Cu+ chaperones, enzymes, or ligands. To address this challenge, we introduce a Cu+ chaperone‐inspired supramolecular approach to disrupt Cu+ homeostasis in cancer cells that induces programmed cell death. The Nap‐FFMTCGGCR peptide self‐assembles into nanofibers inside cancer cells with high binding affinity and selectivity for Cu+ due to the presence of the unique MT/CGGC motif, which is conserved in intracellular Cu+ chaperones. Nap‐FFMTCGGCR exhibits cytotoxicity towards triple negative breast cancer cells (MDA‐MB‐231), impairs the activity of Cu+ dependent co‐chaperone super oxide dismutase1 (SOD1), and induces oxidative stress. In contrast, Nap‐FFMTCGGCR has minimal impact on normal HEK 293T cells. Control peptides show that the self‐assembly and Cu+ binding must work in synergy to successfully disrupt Cu+ homeostasis. We show that assembly‐enhanced affinity for metal ions opens new therapeutic strategies to address disease‐relevant metal ion homeostasis.