Triple negative breast cancer (TNBC) is a highly aggressive, invasive, and metastatic tumor. Although it is reported to be sensitive to cytotoxic chemotherapeutics, frequent relapse and chemoresistance often result in treatment failure. In this study, we developed a biomimetic nanodrug consisting of a self-assembling variant (HFn) of human apoferritin loaded with curcumin. HFn nanocage improved the solubility, chemical stability, and bioavailability of curcumin, allowing us to reliably carry out several experiments in the attempt to establish the potential of this molecule as a therapeutic agent and elucidate the mechanism of action in TNBC. HFn biopolymer was designed to bind selectively to the TfR1 receptor overexpressed in TNBC cells. HFn-curcumin (CFn) proved to be more effective in viability assays compared to the drug alone using MDA-MB-468 and MDA-MB-231 cell lines, representative of basal and claudin-low TNBC subtypes, respectively. Cellular uptake of CFn was demonstrated by flow cytometry and label-free confocal Raman imaging. CFn could act as a chemosensitizer enhancing the cytotoxic effect of doxorubicin by interfering with the activity of multidrug resistance transporters. In addition, CFn exhibited different cell cycle effects on these two TNBC cell lines, blocking MDA-MB-231 in G0/G1 phase, whereas MDA-MB-468 accumulated in G2/M phase. CFn was able to inhibit the Akt phosphorylation, suggesting that the effect on the proliferation and cell cycle involved the alteration of PI3K/Akt pathway.