Eutectic gallium–indium alloy is a promising material for modern microelectronics, medical diagnostics, and flexible robotics. Investigations of the influence of a decrease in the sizes on the properties of the Ga–In alloy are of great interest in view of its novel ranges of applications. In this study, the atomic mobility in the segregated gallium-enriched crystalline phase of a nanostructured Ga–In alloy has been analyzed by NMR. The alloy with a composition of 94 at % Ga and 6 at % In has been introduced into pores of an opal matrix. It is shown that the gallium-enriched phase had a β-Ga structure. The temperature dependence of the nuclear spin–lattice relaxation rate of gallium has been measured. Contributions from the magnetic dipole and electrical quadrupole mechanisms of relaxation are separated. Temperature dependence of the atomic motion correlation time is calculated and the activation energy is estimated.