Deuteron magnetic relaxation rates and self-diffusion coefficients measured by the H-1 spin-echo technique are reported for aqueous solutions of xenon in the temperature range from 273 to 333 K at pressures up to 6 MPa. The data enable the determination of the reorientational correlation time and self-diffusion coefficient of water in the first coordination sphere of xenon and provide the first direct experimental proof of a perceptible slowing down of these motions. At 298 K we find a retardation by a factor of 1.3 of rotational and translational motions in the first hydration shell of xenon above those in the bulk. The data are compared with the results of computer simulations and with estimates extracted from experimental data for alkyl groups in larger molecules. A comparison of results for rotational and translational motions shows that at high temperatures both are affected to the same degree. Below 298 K this strong coupling is lost. This phenomenon appears to be related to known anomalies of water in the supercooled regime, possibly associated with a thermodynamic singularity near T-s = 228 K. Xenon may shift T-s to higher temperatures.