We have observed a Fragile‐to‐Strong Dynamic Crossover (FSC) phenomenon of the α‐relaxation time and self‐diffusion constant in confined supercooled water. The α‐relaxation time is measured by Quasielastic Neutron Scattering (QENS) experiments and the self‐diffusion constant by Nuclear Magnetic Resonance (NMR) experiments. Water is confined in 1‐d geometry in cylindrical pores of nanoscale silica materials, MCM‐41‐S and in Double‐Wall Carbon Nanotubes (DWNT). The crossover phenomenon can also be observed from appearance of a Boson peak in Incoherent Inelastic Neutron Scattering experiments. We observe a pronounced violation of the Stokes‐Einstein Relation at and below the crossover temperature at ambient pressure. Upon applying pressure to the confined water, the crossover temperature is shown to track closely the Widom line emanating from the existence of a liquid‐liquid critical point in an unattainable deeply supercooled state of bulk water. Relation of the dynamic crossover phenomenon to the existence of a density minimum in supercooled confined water is discussed. Finally, we discuss a role of the FSC of the hydration water in a biopolymer that controls the biofunctionality of the biopolymer.