The spin-lattice relaxation times for the $^{115}\mathrm{In}$ isotope in liquid indium embedded into artificial opals and porous glass were found to be shortened remarkably compared to the bulk indium melt. The spin relaxation acceleration was ascribed mainly to the enhancement of the quadrupole contribution caused by the translational diffusion in liquid indium; the magnetic contribution was implied unchanged on the base of the Knight shift measurements and the Korringa relation. Calculations made for quadrupole relaxation showed that it dominated the spin relaxation process for indium in nanopores and that the correlation times of atomic motion increased by more than a factor of 6 depending on pore sizes. The increase in the correlation time evidenced drastic slowing down the atomic diffusion for confined melted indium.