Targeting breast cancer stem cells (BCSCs) offers a promising strategy for breast cancer treatment. We examined the plant alkaloid ellipticine for its efficacy to inhibit the expression of aldehyde dehydrogenase 1 class A1 (ALDH1A1)-positive BCSCs by in vitro and in silico methods. At 3 mM concentration, ellipticine decreased the expression of ALDH1A1-positive BCSCs by 62% (p = 0.073) in the MCF7 cell line and by 53% (p = 0.024) in the SUM159 cell line compared to vehicle-treated cultures. Ellipticine significantly reduced the formation of mammospheres, whereas paclitaxel enhanced mammosphere formation in both the treated cell lines. Interestingly, when treated with a combination of ellipticine and paclitaxel, the percentage of ALDH1A1-positive BCSCs dropped by several fold in vitro. A homology model of Homo sapiens ALDH1A1 was built using the crystal structure of NAD-bound sheep liver class I aldehyde dehydrogenase [PDB ID: 1BXS] as a template. Molecular simulation and docking studies revealed that the amino acids Asn-117 and Asn-121, Glu-249, Cys-302, and Gln-350, present in the active site of human ALDH1A1, played a vital role in interacting with the drug. The present study suggests that ellipticine reduces the proliferation and self-renewal ability of ALDH1A1-positive BCSCs and can be used in combination with a cytotoxic drug like paclitaxel for potential targeting of BCSCs.