The impact of low water concentration of strongly hydrogen-bonded water molecules on the dynamical properties of amorphous terfenadine (TFD) is investigated through complementary molecular dynamics (MD) simulations and dielectric relaxation spectroscopy (DRS) experiments. In this article, we especially highlight the important role played by some residual water molecules in the concentration of 1−2% (w/w) trapped in the TFD glassy matrix, which are particularly difficult to remove experimentally without a specific heating/drying process. From MD computations and analyses of the hydrogen bonding (HB) interactions, different categories of water molecules are revealed and particularly the presence of strongly HB water molecules. These latter localize themselves in small pockets in empty spaces existing in between the TFD molecules due to the poor packing of the glassy state and preferentially interact with the polar groups close to the flexible central part of the TFD molecules. We present a simple model which rationalizes at the molecular scale the effect of these strongly HB water molecules on dynamics and how they give rise to a supplementary relaxation process (namely process S) which is detected for the first time in the glassy state of TFD annealed at room temperature while this process is completely absent in a non-annealed glass. It also explains how this supplementary relaxation is coupled with the intramolecular motion (namely process γ) of the very flexible central part of the TFD molecule. The present findings help to understand more generally the microscopic origin of the secondary relaxations often detected by DRS in the glassy states of molecular compounds for which the exact nature is still debated.