Aqueous solutions of sodium L-glutamate (NaGlu) in the concentration range 0 < c/M ≤ 1.90 at 25 °C were investigated by dielectric relaxation spectroscopy (DRS) and statistical mechanics (1D-RISM and 3D-RISM calculations) to study the hydration and dynamics of the L-glutamate (Glu⁻) anion. Although at c → 0 water molecules beyond the first hydration shell are dynamically affected, Glu⁻ hydration is rather fragile and for c ≳ 0.3 M apparently restricted to H₂O molecules hydrogen bonding to the carboxylate groups. These hydrating dipoles are roughly parallel to the anion moment, leading to a significantly enhanced effective dipole moment of Glu⁻. However, L-glutamate dynamics is determined by the rotational diffusion of individual anions under hydrodynamic slip boundary conditions. Thus, the lifetime of the hydrate complexes, as well as of possibly formed [Na⁺Glu⁻]⁰ ionpairs and L-glutamate aggregates, cannot exceed the characteristic timescale for Glu⁻ rotation.