Using dielectric spectroscopy experiments performed at multiple temperatures and frequency ranges, we demonstrate how the chemotherapy drug paclitaxel changes the dynamic properties of water in a breast cancer cell line (MCF-7). From the measured data, we present evidence that treatment with paclitaxel leads to a slight increase in activation energy in a relaxation related to bulk-like water. More importantly, we also observe that paclitaxel changes the constraining imposed by the biological interfaces on hydration water, whose single-particle dynamics becomes slower and with higher activation energy. These variations are only observable after freezing the dynamics from other cellular components, such as proteins and DNAs, regardless of the state of the cells, that is, treated or not treated or even if the cells are no longer viable. Therefore, changes in water dynamics could be detected prior to those related to the global dynamics within the cellular environment.