A model of two-dimensional water is studied in order to analyze recent dielectric measurements on protein hydration water. The frustration introduced by the coupling of the water molecules to the protein surface prevents a true crystallization and induces a smooth transition to a glassy state that is detected by its structure factor and the stretched exponential behavior of the cage correlation function that measures the rate of change of the hydrogen bond network around each molecule. The spectrum of the fluctuations in the vicinity of the glass transition exhibits 1/f(alpha) noise in agreement with the dielectric measurements. The results suggest that two-dimensional water, which can be probed by dielectric measurements, could be an interesting system to study the glassy behavior of water.