Breast cancer is the most-diagnosed cancer type among women. The triple-negative subtype is an especially aggressive type of breast cancer. Although chemotherapy is almost the only option for the treatment of triple-negative breast cancer (TNBC), currently used chemotherapeutics are not effective enough, considering the poor survival rate of patients. Therefore, novel compounds need to be developed to improve survival rates. It has been known that quinonic compounds, which are found in nature, have antibacterial, antifungal, and antitumorigenic properties. Naphthoquinones are members of the quinone family and are widely used in research due to their promising properties. In this study, we evaluated the cytotoxic activity of a novel naphthoquinone-derived compound (1,4-naphthoquinone (1,4-NQ)) against two different breast cancer cells: a hormone-responsive cell line (MCF-7) and a triple-negative cell line (MDA-MB-231). As a result, 1,4-NQ decreased cell viability in both tested cell lines in a dose-dependent manner. Increased apoptotic markers (presence of pyknotic nuclei, annexin-V positivity, caspase 3/7 activity, and decreased mitochondrial membrane potential) and DNA damage were especially observed in MDA-MB-231 cells after treatment with the compound. Considering the promising cytotoxic effect of the compound, 1,4-NQ needs further evaluation as a potential candidate for the treatment of TNBC.