A β-NMR study was performed on a Sr2RuO4 crystal in the metallic state using a beam of spin-polarized 8Li+ implanted at a mean depth of 90 nm. The 8Li+ spin-lattice relaxation rate is strongly influenced by the onset of incommensurate spin fluctuations. The nuclear relaxation rate can be explained using previously published bulk 17O NMR and inelastic neutron spectroscopy measurements of the dynamic magnetic susceptibility to model the hyperfine coupling. A well-resolved quadrupolar-split NMR for 8Li+ implies a static stopping position in an interstitial site. The 8Li+ Knight shift is highly sensitive to the anisotropic static susceptibility.