Colorectal cancer (CRC), breast cancer, and chronic myeloid leukemia (CML) are life-threatening malignancies worldwide. Although potent therapeutic and screening strategies have been developed so far, these cancer types are still major public health problems. Therefore, the exploration of more potent and selective new agents is urgently required for the treatment of these cancers. Quinones represent one of the most important structures in anticancer drug discovery. We have previously identified a series of quinone-based compounds (ABQ-1-17) as anti-CML agents. In the current work, ABQ-3 was taken to the National Cancer Institute (NCI) for screening to determine its in vitro antiproliferative effects against a large panel of human tumor cell lines at five doses. ABQ-3 revealed significant growth inhibition against HCT-116 CRC and MCF-7 breast cancer cells with 2.00 µM and 2.35 µM GI50 values, respectively. The MTT test also showed that ABQ-3 possessed anticancer effects towards HCT-116 and MCF-7 cells with IC50 values of 5.22 ± 2.41 μM and 7.46 ± 2.76 μM, respectively. Further experiments indicated that ABQ-3 induced apoptosis in both cell lines, and molecular docking studies explicitly suggested that ABQ-3 exhibited DNA binding in a similar fashion to previously reported compounds. Based on in silico pharmacokinetic prediction, ABQ-3 might display drug-like features enabling this compound to become a lead molecule for future studies.