By means of a nuclear magnetic resonance experiment, we give evidence of the existence of a fragile-to-strong dynamic crossover transition (FST) in confined water at a temperature T(L)=223+/-2 K. We have studied the dynamics of water contained in 1D cylindrical nanoporous matrices (MCM-41-S) in the temperature range 190-280 K, where experiments on bulk water were so far hampered by crystallization. The FST is clearly inferred from the T dependence of the inverse of the self-diffusion coefficient of water (1D) as a crossover point from a non-Arrhenius to an Arrhenius behavior. The combination of the measured self-diffusion coefficient D and the average translational relaxation time tau(T), as measured by neutron scattering, shows the predicted breakdown of Stokes-Einstein relation in deeply supercooled water.