Water-soluble amphiphilic polymers are vital chemicals in the oil and gas industry to retard crystal growth of hydrocarbon hydrate via surface adsorption and suppress nucleation of a pristine hydrate nucleus, thereby preventing formation of hydrate blockages in flow lines during oil and natural gas production. Apart from a few theoretical modeling studies, an experimental method to study the polymer/water interface in the crystal growth is critically needed. Here, water motions in the hydration shells of an exemplary kinetic inhibitor, poly(N-vinylcaprolactam), during hydrate formation from the tetrahydrofuran/water system are revealed via nuclear magnetic resonance relaxometry. Unequivocal experiments show that the pivotal interfacial water in the tightly bound state gradually freezes at rates depending on the polymer molecular weight (MW). This is supported by nonfreezable water analysis, which is correlated to the inhibition time. The polymers tune the kinetics of the hydration process via interaction with and perturbation of the water molecules. The free water component in the polymer solution crystallizes at a very slow rate when in partially restricted mobility, whereas the bound water component increases in the reaction, with the polymer/water interface serving as the reaction sites. The appropriate MW (including average MW and polydispersity values) of the inhibitive polymers can give rise to maximal retardation of the hydrate crystal growth. This work will help control other multiphase crystallization kinetic processes through the design of inhibitors or promoters functioning in the interface.