Breast cancer (BC) is one of the main types of cancer that endangers women’s lives. The characteristics of triple-negative breast cancer (TNBC) include a high rate of recurrence and the capacity for metastasis; therefore, new therapies are urgently needed to combat TNBC. Dual targeting HDAC6 and Hsp90 has shown good synergistic effects in treating metastatic TNBC. The goal of this study was to find potential HDAC6 and Hsp90 dual inhibitors. Therefore, several in silico approaches have been used. An e-pharmacophore model generation based on the HDAC6-ligand complex and subsequently a pharmacophore-based virtual screening on 270,450 natural compounds from the ZINC were performed, which resulted in 12,663 compounds that corresponded to the obtained pharmacophoric hypothesis. These compounds were docked into HDAC6 and Hsp90. This resulted in the identification of three compounds with good docking scores and favorable free binding energy against the two targets. The top three compounds, namely ZINC000096116556, ZINC000020761262, and ZINC000217668954, were further subjected to ADME prediction and molecular dynamic simulations, which showed promising results in terms of pharmacokinetic properties and stability. As a result, these three compounds can be considered potential HDAC6 and Hsp90 dual inhibitors and are recommended for experimental evaluation.