Breast cancer is the most common cancer among women, contributing to 32.1% of cases in Argentina (Globocan2020). Triple-negative breast cancer (TNBC) is an aggressive subtype of breast cancer characterized by high invasiveness, high metastatic potential, propensity for relapse, and poor prognosis. Consequently, developing innovative TNBC therapeutic strategies has become essential for clinical practice. Here we demonstrated the anticancer potency of our most recently synthesized and reported Cu(II) complex derived from acylhydrazone, [Cu(N−N−Fur)(NO3)(H2O)] (CuHL1), on a panel of human TNBC cell lines each distinctive features (MDA-MB-231, MDA-MB-157, MDA-MB-468 and HCC1806). CuHL1 presented a highly cytotoxic effect on all cells tested, showing IC50 values between 1.5 and 2.7 µM at 24 h of treatment. Further analyses were carried out on MDA-MB-231 cells to reveal the mechanism of action of the complex. CuHL1 produced an increment of reactive oxygen species from 1 µM when tested after 3 h of incubation. This complex also induced apoptosis cell death, as can be seen by an augment of early apoptotic cells at 1 µM and an increment of late apoptotic cells at 1 and 2.5 µM after 24 h treatment. Finally, proteomic analysis was performed through label-free quantification using the Orbitrap LC-MS/MS (Thermo ScientificTM, Waltham, MA, USA). Among the 34 differentially expressed proteins, 19 were up- and 15 down-regulated by the treatment with 1 µM of CuHL1. Interestingly, BCAR3 (Breast cancer anti-estrogen resistance 3) was down-regulated and it was reported previously that high BCAR3 mRNA expression, specifically in TNBC, correlates with poorer outcomes and chemoresistance effects in patients. Despite it would be necessary to carry out other proteomic assays to validate our results, CuHL1 is positioned as a promising candidate for potential anti-TNBC therapies and would be attractive to further test this complex on in vivo studies.