Ginger-derived compounds are abundant sources of anticancer natural products. However, the anticancer effects of (E)-3-hydroxy-1-(4′-hydroxy-3′,5′-dimethoxyphenyl)-tetradecan-6-en-5-one (3HDT) have not been examined. This study aims to assess the antiproliferation ability of 3HDT on triple-negative breast cancer (TNBC) cells. 3HDT showed dose-responsive antiproliferation for TNBC cells (HCC1937 and Hs578T). Moreover, 3HDT exerted higher antiproliferation and apoptosis on TNBC cells than on normal cells (H184B5F5/M10). By examining reactive oxygen species, mitochondrial membrane potential, and glutathione, we found that 3HDT provided higher inductions for oxidative stress in TNBC cells compared with normal cells. Antiproliferation, oxidative stress, antioxidant signaling, and apoptosis were recovered by N-acetylcysteine, indicating that 3HDT preferentially induced oxidative-stress-mediated antiproliferation in TNBC cells but not in normal cells. Moreover, by examining γH2A histone family member X (γH2AX) and 8-hydroxy-2-deoxyguanosine, we found that 3HDT provided higher inductions for DNA damage, which was also reverted by N-acetylcysteine. In conclusion, 3HDT is an effective anticancer drug with preferential antiproliferation, oxidative stress, apoptosis, and DNA damage effects on TNBC cells.