Triple-negative breast cancer (TNBC) is a very aggressive disease even in its early stages and is characterized by a severe prognosis. Neoadjuvant chemotherapy is one of the milestones of treatment, and paclitaxel (PTX) is among the most active drugs used in this setting. However, despite its efficacy, peripheral neuropathy occurs in approximately 20–25% of cases and represents the dose-limiting toxicity of this drug. New deliverable strategies to ameliorate drug delivery and reduce side effects are keenly awaited to improve patients’ outcomes. Mesenchymal stromal cells (MSCs) have recently been demonstrated as promising drug delivery vectors for cancer treatment. The aim of the present preclinical study is to explore the possibility of a cell therapy approach based on the use of MSCs loaded with PTX to treat TNBC-affected patients. For this purpose, we in vitro evaluated the viability, migration and colony formation of two TNBC cell lines, namely, MDA-MB-231 and BT549, treated with MSC-PTX conditioned medium (MSC-CM PTX) in comparison with both CM of MSCs not loaded with PTX (CTRL) and free PTX. We observed stronger inhibitory effects on survival, migration and tumorigenicity for MSC-CM PTX than for CTRL and free PTX in TNBC cell lines. Further studies will provide more information about activity and potentially open the possibility of using this new drug delivery vector in the context of a clinical study.