Histone deacetylases (HDACs) are an attractive drug target for the treatment of human breast cancer (BC), and therefore, HDAC inhibitors (HDACis) are being used in preclinical and clinical studies. The need to understand the scope of the mode of action of HDACis, as well as the report of the co-crystal structure of HDAC6/SS-208 at the catalytic site, provoked us to develop an isoxazole-based lead structure called 4-(2-(((1-(3,4-dichlorophenyl)-1H-1,2,3-triazol-4-yl)methyl)thio) pyrimidin-4-yl) morpholine (5h) and 1-(2-(((3-(p-tolyl) isoxazol-5-yl)methyl)thio) pyrimidin-4-yl) piperidin-4-one (6l) that targets HDACs in human BC cells. We found that the compound 5h or 6l could inhibit the proliferation of BC cells with an IC50 value of 8.754 and 11.71 µM, respectively. Our detailed in silico analysis showed that 5h or 6l compounds could target HDAC in MCF-7 cells. In conclusion, we identified a new structure bearing triazole, isoxazole, and thiouracil moiety, which could target HDAC in MCF-7 cells and serve as a base to make new drugs against cancer.