Tumor progression may be driven by a small subpopulation of cancer stem cells (CSCs characterized by CD44+/CD24− phenotype). We investigated the influence of a newly developed thienopyridine anticancer compound (3-amino-5-oxo-N-naphthyl-5,6,7, 8-tetrahydrothieno[2,3-b]quinoline-2-carboxamide, 1) on the growth, survival and glycophenotype (CD15s and GM3 containing neuraminic acid substituted with acetyl residue, NeuAc) of breast and prostate cancer stem/progenitor-like cell population. MDA-MB-231 and Du-145 cells were incubated with compound 1 alone or in combination with paclitaxel. The cellular metabolic activity was determined by the 3-(4,5-dimethylthiazolyl-2)-2,5-diphenyltetrazolium bromide (MTT) assay. The type of cell death induced by 48-h treatment was assessed using a combination of Annexin-V-FITC and propidium iodide staining. Flow cytometric analysis was performed to detect the percentage of CD44+/CD24− cells, and GM3 and CD15s positive CSCs, as well as the expression of GM3 and CD15s per one CSC, in both cell lines. Compound 1 produces a dose- and time-dependent cytotoxicity, mediated mainly by apoptosis in breast cancer cells, and slightly (2.3%) but statistically significant lowering breast CSC subpopulation. GM3 expression per one breast CSC was increased, and the percentage of prostate GM3+ CSC subpopulation was decreased in cells treated with compound 1 compared with non-treated cells. The percentage of CD15s+ CSCs was lower in both cell lines after treatment with compound 1. Considering that triple-negative breast cancers are characterized by an increased percentage of breast CSCs and knowing their association with an increased risk of metastasis and mortality, compound 1 is a potentially effective drug for triple-negative breast cancer treatment.